[User]
How many solutions does the equation (3(2cos(3π(3|(-2x + 2) + 2| - 2) - 1) + 2) - 2)/(-3(2cos(3π(3|(-2x + 2) + 2| - 2) - 1) + 2) + 4) = -3|(-4(-1sin(3πx) + 3)^2 - 2(-1sin(3πx) + 3) - 2) + 3| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1cos(2π((-2(4(-2|x - 3| + 2)^2 - 5(-2|x - 3| + 2) + 1) - 3)/(-3(4(-2|x - 3| + 2)^2 - 5(-2|x - 3| + 2) + 1) + 1)) - 2) + 2 and g(x) = 3|((-2(-1x + 2))/(1(-1x + 2) + 3)) - 2| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(-1|(2x - 3)| - 1) - 2)/(-1(-1|(2x - 3)| - 1) - 2) and g(x) = -3(2cos(3πx + 3) - 2) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2cos(1π(2(2|(4x + 5) - 2| + 2)^2 - 5(2|(4x + 5) - 2| + 2) + 1) + 1) + 3 and g(x) = (-3(2|(-2x - 2) + 3| + 3) - 1)/(-2(2|(-2x - 2) + 3| + 3) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1cos(1π((-3x)/(3x)) + 1) - 3 and g(x) = 2x^2 + 2x - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(-2|(-2(-3x + 1)^2 - 3(-3x + 1) + 5) - 2| + 1) + 2)/(-2(-2|(-2(-3x + 1)^2 - 3(-3x + 1) + 5) - 2| + 1)) and g(x) = -1|(1cos(2π((-2x - 1)/(-1x - 3)) + 1) + 3) + 2| in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(-1|((-3x - 2)/(-1x + 2)) - 3| + 2) + 4 and g(x) = -4((2x + 2)/(1x + 1)) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(-2sin(3π(5x + 4)) + 3) - 2| - 3 and g(x) = -2|(5x - 5) - 1| - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|(-4((2(-2x^2 + 2x + 5))/(-3(-2x^2 + 2x + 5) + 4))) + 1| and g(x) = -5(-4(-2|x + 2| + 1)^2 + 1(-2|x + 2| + 1) + 5) + 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(3π((-2x - 1)/(-1x - 2)) + 1) - 3 and g(x) = -1x^2 - 1x + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(3(-3sin(1πx - 3) - 1)^2 - 5(-3sin(1πx - 3) - 1) - 3) = 5((-3x + 2)/(1x + 3)) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3cos(2π(-3x + 1) - 3) + 1 and g(x) = -2|x - 1| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(1|(-4x) + 1| - 1)^2 + 3(1|(-4x) + 1| - 1) + 5 = -1|(2cos(1πx + 3) - 2) + 1| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1((2(-2sin(3πx - 2) - 1))/(1(-2sin(3πx - 2) - 1) + 2))^2 - 4((2(-2sin(3πx - 2) - 1))/(1(-2sin(3πx - 2) - 1) + 2)) + 1 and g(x) = -4((-2x + 1)/(2x + 1))^2 + 2((-2x + 1)/(2x + 1)) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(-4(2((-1x)/(-1x + 2)) + 5)^2)| + 1 and g(x) = -1sin(3π(-5(1|x + 1|)^2 + 3(1|x + 1|) + 2) - 3) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(1((3(1x^2 + 5x + 3))/(-2(1x^2 + 5x + 3) - 2)) - 1) - 1| + 3 and g(x) = (-3(-4(-1e^(2x) + 1) + 4))/(-1(-4(-1e^(2x) + 1) + 4) - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|((3(-5(-2x^2 + 2x + 1) + 4))/(1(-5(-2x^2 + 2x + 1) + 4) - 3)) + 3| + 1 and g(x) = -2|(2(-3e^(1x) + 2) - 3) + 2| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2e^(-1((-1(-2|(-1x^2 + 1x + 2)|) - 1)/(2(-2|(-1x^2 + 1x + 2)|) - 1))) + 2 = 1|(-1((1x + 1)/(3x)) + 2) - 1| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-2x + 1)^2 + 1(-2x + 1) - 5 and g(x) = 2|x + 3| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(-2e^(-2x) - 2) + 2| - 3 and g(x) = -3|x - 3| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2((-3(3|(3sin(2πx) + 3) - 2| + 2) + 3)/(-2(3|(3sin(2πx) + 3) - 2| + 2)))^2 - 4 and g(x) = -5(2(1e^(1x))^2 - 5(1e^(1x)) + 2) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(1x - 4)^2 + 3(1x - 4) + 1 and g(x) = 2x - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(-3|x + 3| + 1)^2 - 5(-3|x + 3| + 1) - 4 and g(x) = 3x^2 + 2x - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(-1((-2x + 3)/(-1x + 2))^2 - 5((-2x + 3)/(-1x + 2)) + 4) + 5 and g(x) = 2(-3|x + 3| - 1)^2 + 2(-3|x + 3| - 1) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1|(3((1(3x))/(-1(3x) + 2))^2 - 1((1(3x))/(-1(3x) + 2)) + 3) + 2| + 1 = -3|(2((1x)/(2x + 2)) - 3)| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3((1(4(1|x + 3| + 3)^2) - 2)/(-1(4(1|x + 3| + 3)^2) - 3)) + 5 and g(x) = -3cos(1π(-1|(5x + 3) + 3|) - 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(-2sin(2πx) - 3) - 3 and g(x) = 4x^2 + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2sin(1π(1x^2 - 3x - 1) - 3) + 3 and g(x) = 3|x + 2| - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(1x^2 + 5x + 3) + 4 and g(x) = -1x + 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(2|(-5x - 2) + 3|) + 2)/(3(2|(-5x - 2) + 3|) - 1) and g(x) = -2|(2x + 4) + 2| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(2e^(2x) + 1) + 3)/(2(2e^(2x) + 1) + 2) and g(x) = -1|x + 1| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(-3|(1cos(2πx) + 2) - 3| - 2) + 3)/(3(-3|(1cos(2πx) + 2) - 3| - 2) + 2) = 1(1x^2 - 5x + 4) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(-4(2|(3x^2 + 3x - 3) - 2| - 1) + 4) + 3)/(-2(-4(2|(3x^2 + 3x - 3) - 2| - 1) + 4) - 1) = -1(-2cos(2π(-2|x - 2| - 1) + 1) - 1)^2 - 1(-2cos(2π(-2|x - 2| - 1) + 1) - 1) + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(-1|(2(4x^2 - 5x - 3) + 1) - 3| + 3) - 3)/(-2(-1|(2(4x^2 - 5x - 3) + 1) - 3| + 3) - 1) and g(x) = -1|((1(-1x^2 + 4x - 3) - 1)/(-3(-1x^2 + 4x - 3)))| - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(-1((1x + 1)/(1x)) - 1) - 2| - 3 and g(x) = (-3(-1x^2 - 4x + 2) - 2)/(3(-1x^2 - 4x + 2) + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(1|(-2((-2x + 3)/(-1x + 2))) - 3| - 1)^2 - 4(1|(-2((-2x + 3)/(-1x + 2))) - 3| - 1) - 5 = 5(-1e^(1((3x)/(-3x + 1))) + 2)^2 + 1(-1e^(1((3x)/(-3x + 1))) + 2) + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(1|(1(-3x - 1)^2 + 1(-3x - 1) - 5) - 1| - 1) - 3)/(3(1|(1(-3x - 1)^2 + 1(-3x - 1) - 5) - 1| - 1) - 2) and g(x) = 3sin(1π((-2(4x^2 + 2x + 1) - 3)/(-2(4x^2 + 2x + 1) - 3)) - 1) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(1|(-3x^2 + 5x - 1) + 2| + 2) - 3)/(-3(1|(-3x^2 + 5x - 1) + 2| + 2) - 3) = 3cos(3π(4x^2 + 3x + 1) - 2) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5(3x^2 - 3x - 1) - 2 and g(x) = -1|x + 1| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1|(-5(3((-2x + 1)/(3x))^2 - 1) - 5) + 3| and g(x) = 2|((1(3cos(1πx - 2) + 2) + 2)/(2(3cos(1πx - 2) + 2))) - 1| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(-2|(1((3x - 2)/(2x))^2 + 4((3x - 2)/(2x))) + 1| + 2) + 3 and g(x) = -4(-3cos(1π(-4x^2 + 2x + 3) - 2) + 2) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(-1(-3cos(1π(-2|x| + 2) + 3) - 1)^2 + 5(-3cos(1π(-2|x| + 2) + 3) - 1) + 3) - 2)/(-2(-1(-3cos(1π(-2|x| + 2) + 3) - 1)^2 + 5(-3cos(1π(-2|x| + 2) + 3) - 1) + 3) - 1) = 2|(-3(-2cos(1πx + 1) + 2)^2 + 3(-2cos(1πx + 1) + 2) + 2) + 2| + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2cos(1π((3(3(1x^2 + 1x) - 3) - 2)/(3(3(1x^2 + 1x) - 3) - 2)) + 3) - 2 = -2|(-1((-2x - 3)/(1x))) + 3| - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(3cos(2πx - 2) + 1)^2 - 2(3cos(2πx - 2) + 1) - 3 and g(x) = -1x - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(2sin(3π((-3x - 2)/(1x + 2))) + 2) + 2 = 3|(4x^2 + 1x + 3) - 2| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1|((3x - 1)/(2x - 1)) + 3| + 2 and g(x) = 1x - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(2cos(2π(-3|x - 3| - 1) - 1) - 2)^2 + 2(2cos(2π(-3|x - 3| - 1) - 1) - 2) - 3 and g(x) = (2(1x^2 + 3x + 5) - 2)/(1(1x^2 + 3x + 5)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(1π(1|x + 2| + 1) - 2) + 3 and g(x) = 1x - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4((-2(-1x^2 + 4) - 1)/(3(-1x^2 + 4) - 2)) - 2 and g(x) = 1|(2sin(3πx - 1) + 2) - 1| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|((2(-2(-3x + 3)^2 + 2(-3x + 3) + 4) + 3)/(-3(-2(-3x + 3)^2 + 2(-3x + 3) + 4) + 2)) + 2| - 1 and g(x) = (-3(3(4x + 4)^2 + 5(4x + 4) + 3) + 2)/(1(3(4x + 4)^2 + 5(4x + 4) + 3)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(3cos(2πx + 2) + 3) - 2| + 2 and g(x) = -5x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(2π((-2x)/(-1x + 3)) - 2) + 1 and g(x) = 5x^2 + 4x - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3|(-4x^2 - 3x + 4)| - 3 = (2x + 1)/(2x - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(1(1|((2x - 1)/(1x)) + 2| - 1)^2 + 2(1|((2x - 1)/(1x)) + 2| - 1) - 2) - 2 and g(x) = -1(1((1x + 1)/(-2x - 1)) + 5)^2 - 4(1((1x + 1)/(-2x - 1)) + 5) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3(3e^(1x) - 2) - 1 and g(x) = 5x^2 - 1x - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(2|(4(1e^(-2x) - 1)^2 + 1(1e^(-2x) - 1) - 3) + 2| + 3) + 2)/(-3(2|(4(1e^(-2x) - 1)^2 + 1(1e^(-2x) - 1) - 3) + 2| + 3) - 2) and g(x) = (-2(-1|(1x^2 - 2x - 4) + 3| + 2))/(-1(-1|(1x^2 - 2x - 4) + 3| + 2) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(-3|x| - 2) + 1)/(-2(-3|x| - 2) + 1) = -1|x - 2| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3|(3(-3x^2 + 1x + 4) + 4) + 2| + 3 and g(x) = -1cos(2π(-3x^2 + 3x - 2) - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|((-1x - 3)/(-1x)) + 2| and g(x) = -1x + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3|(1x^2) - 2| + 3 and g(x) = 4x^2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1sin(3π(1|(1x^2 + 5x - 1)| - 1) - 3) + 3 and g(x) = 2cos(2π(-2x + 5) + 3) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2|(-2sin(3πx + 1) - 1) - 1| + 3 and g(x) = 3|x + 2| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4(-2cos(1π(3|x - 3| - 1)) - 3)^2 - 4(-2cos(1π(3|x - 3| - 1)) - 3) and g(x) = 2(-2e^(-1x) - 1) - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(2π(1(1x - 2)^2 + 5(1x - 2) + 1) + 1) - 3 = 1|((2x + 1)/(2x)) - 3| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(-4(-4x^2 - 2x + 5) + 3) - 2)/(-1(-4(-4x^2 - 2x + 5) + 3) + 3) and g(x) = -4(-5x^2 + 1x - 4) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(2e^(2(-2x^2 - 4x - 5)) + 2) + 3)/(-1(2e^(2(-2x^2 - 4x - 5)) + 2) - 3) and g(x) = -2cos(2π((3x + 3)/(2x + 3)) - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(-1|(5(1x - 1)^2 - 5(1x - 1) + 2) + 2| - 3) + 2)/(-2(-1|(5(1x - 1)^2 - 5(1x - 1) + 2) + 2| - 3) + 1) and g(x) = -1|(2(2x - 4)^2 + 5(2x - 4)) - 1| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1((-2(5x + 3) + 3)/(1(5x + 3)))^2 + 5((-2(5x + 3) + 3)/(1(5x + 3))) + 5 and g(x) = 5(-1|x| + 1) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(2sin(1πx) - 1)^2 + 2(2sin(1πx) - 1) - 5 and g(x) = -3|x + 3| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2cos(2π(-3x^2 - 5x - 2) + 3) - 2 and g(x) = -1|x - 1| + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(2π((2x)/(2x))) - 2 and g(x) = 1|x + 1| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2sin(3π((-1x - 1)/(2x - 3))) and g(x) = -5x^2 - 5x + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(1|(-3e^(-1x) - 1) - 1| + 1) + 1 and g(x) = (-3(-3cos(1πx + 3) + 3))/(3(-3cos(1πx + 3) + 3) - 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 5(3cos(2π(5((2x + 2)/(3x + 3))^2 + 4((2x + 2)/(3x + 3))) - 3)) + 5 and g(x) = 1(-3|(1x^2 + 4x - 4) - 3| + 1) - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(3π(3(-4((1x - 1)/(2x - 1))^2 + 1((1x - 1)/(2x - 1)) - 2) + 3) + 3) + 1 and g(x) = 2(-4((1x + 3)/(1x - 2))^2 - 5((1x + 3)/(1x - 2)) - 1) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(3π((-3x + 3)/(-2x - 3)) - 1) and g(x) = 1|x - 1| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(1(-1|x|)^2 - 5(-1|x|) - 2) - 2)/(3(1(-1|x|)^2 - 5(-1|x|) - 2) + 3) and g(x) = -2|(-1x - 3) - 1| + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(-5x^2 - 2x + 5) + 2 and g(x) = -3x + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(1|(3(-3x - 3)^2 - 5(-3x - 3) + 1)|) + 2)/(-2(1|(3(-3x - 3)^2 - 5(-3x - 3) + 1)|) + 3) and g(x) = -4(-4((-3x + 1)/(-1x - 3))^2 - 4((-3x + 1)/(-1x - 3)) + 1) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(-3cos(2π(-5x^2 - 3x + 3) - 1)) - 2 and g(x) = 3|(-1x - 5) + 2| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(-1|((-2(-3x))/(-2(-3x) + 3)) + 3| + 3)^2 - 2(-1|((-2(-3x))/(-2(-3x) + 3)) + 3| + 3) - 1 and g(x) = 1sin(3π(-1(1|x - 3| + 1) + 2) + 3) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4(3sin(2πx) + 1)^2 - 4(3sin(2πx) + 1) + 1 = (2x + 1)/(2x - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(3cos(1π(-2((-1x + 2)/(2x + 2)) - 4) + 2) + 2) - 1| and g(x) = -2(-2cos(2π(3|x + 3| - 3) + 2) + 1)^2 + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(1|(2x^2 + 3x - 5)| + 2))/(-1(1|(2x^2 + 3x - 5)| + 2) + 3) and g(x) = 3|(5x^2 - 2x + 1) - 3| - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2e^(2(-2|x + 1| + 1)) - 2 = (-1x - 2)/(-1x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|(1((-2x + 3)/(-2x - 1)) - 1) + 2| and g(x) = -2(1|x + 3| + 1) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(3x^2 - 2x + 4) + 3)/(-1(3x^2 - 2x + 4) - 2) and g(x) = -1x^2 + 3x + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(-2cos(1π(2|(4x^2 - 4x + 3) + 2| - 3) + 2) - 3) - 1)/(-2(-2cos(1π(2|(4x^2 - 4x + 3) + 2| - 3) + 2) - 3) + 1) and g(x) = -3(3|(4x^2 - 1x - 5) + 3| - 2) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(-2sin(1π((3(-1x^2 + 5x + 5) - 1)/(1(-1x^2 + 5x + 5) - 2)) - 2) + 3) and g(x) = (-1(3|(-4x) + 1|) - 1)/(3(3|(-4x) + 1|) - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-2(1(-3cos(3πx - 2))^2 - 1(-3cos(3πx - 2)) + 4))/(-2(1(-3cos(3πx - 2))^2 - 1(-3cos(3πx - 2)) + 4) - 1) and g(x) = -4(-3x^2 - 4x + 1) - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2((-3(-4x - 2) + 1)/(2(-4x - 2)))^2 - 3((-3(-4x - 2) + 1)/(2(-4x - 2))) + 1 and g(x) = -2(1|x + 2| + 1)^2 + 5(1|x + 2| + 1) - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|((-2(3x^2 + 2x - 3) - 2)/(-1(3x^2 + 2x - 3))) + 1| + 3 and g(x) = 2(-3x - 3)^2 + 4(-3x - 3) - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(-2sin(1π(1x^2 + 1x + 3) + 1) - 2) - 4 = 1(-5x^2 + 5x + 5) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(-2sin(1πx + 2) + 3) - 3| - 2 = -1x^2 - 4x + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2((-2(-1e^(1x) + 2) - 3)/(-1(-1e^(1x) + 2) - 1))^2 + 4((-2(-1e^(1x) + 2) - 3)/(-1(-1e^(1x) + 2) - 1)) + 4 and g(x) = 2(-1cos(1πx - 1) + 3) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1|(-2x - 3) - 3| + 3 and g(x) = 3|x + 1| + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|(1x) + 1| + 2 and g(x) = (1x - 1)/(3x - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(3x + 3)^2 - 5(3x + 3) - 4 = (-1x - 1)/(-3x - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(-1|(-2cos(3π(1x + 5)) + 3) - 1| + 2)^2 - 4(-1|(-2cos(3π(1x + 5)) + 3) - 1| + 2) - 5 and g(x) = (-3(-2|(-5x - 3) - 3| - 1) - 1)/(-3(-2|(-5x - 3) - 3| - 1)) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(-2sin(2π(1|x| - 3) - 2)) - 1)/(-3(-2sin(2π(1|x| - 3) - 2)) + 1) and g(x) = 3e^(2((2x - 2)/(3x + 1))) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(-2(-3sin(3πx - 1) - 2)^2 - 4(-3sin(3πx - 1) - 2) + 4) + 2 and g(x) = -1|(3x + 2) + 1| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(-2cos(2πx + 2)) - 3)/(-2(-2cos(2πx + 2)) - 2) and g(x) = -3x + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|(-3((-1(-4x^2 - 4x + 4) - 2)/(-2(-4x^2 - 4x + 4) + 3)) + 3)| + 3 and g(x) = -1e^(-1((1(1|x + 3| + 1) - 1)/(-2(1|x + 3| + 1) + 1))) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 5(-3e^(-1(2|x - 1| - 3)) + 2)^2 + 4(-3e^(-1(2|x - 1| - 3)) + 2) + 1 = 4(-2e^(1x) + 3) - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1cos(3π(2|((-2x + 1)/(1x + 1))| - 2)) - 2 and g(x) = -1cos(1π(5x^2 + 3x + 4) - 1) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(-5x^2 + 3x + 5))/(-3(-5x^2 + 3x + 5) - 2) and g(x) = (-1x)/(-1x - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(-3sin(3π(-1|x - 1| - 3)) - 1)^2 - 5(-3sin(3π(-1|x - 1| - 3)) - 1) + 2 and g(x) = 2|((-2x + 2)/(-1x - 2))| + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3e^(-1(-5(-2|x| - 3) - 3)) and g(x) = -1(2cos(3πx - 1)) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5(-3|((3x + 1)/(-3x)) - 3| - 1)^2 + 5(-3|((3x + 1)/(-3x)) - 3| - 1) and g(x) = -3(3|x| - 2)^2 + 3(3|x| - 2) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(2|(-3e^(2x) - 3) - 2| + 1) + 3)/(-3(2|(-3e^(2x) - 3) - 2| + 1) + 2) and g(x) = -2((1x + 2)/(1x - 3))^2 - 4((1x + 2)/(1x - 3)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-2(-5(3|x - 2| - 2)^2 - 4(3|x - 2| - 2) - 1) - 3)/(2(-5(3|x - 2| - 2)^2 - 4(3|x - 2| - 2) - 1)) and g(x) = -2(-2cos(1πx + 1) + 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(-1x + 1) + 2| and g(x) = -1x - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(-2sin(2π(-2|x + 3| + 1) + 2) - 3) - 3)/(-1(-2sin(2π(-2|x + 3| + 1) + 2) - 3)) and g(x) = 2(-2x - 2)^2 + 4(-2x - 2) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(4(-1cos(2π(2x^2 - 2x + 3) + 1) - 3) - 4)| and g(x) = -2|(5((2x)/(-2x + 3))^2 + 5) - 1| in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(-1((3(1|x - 2| - 1) - 2)/(3(1|x - 2| - 1) - 1))^2 + 4((3(1|x - 2| - 1) - 2)/(3(1|x - 2| - 1) - 1)) - 4) and g(x) = -2cos(2π(3|((1x - 1)/(-2x - 3)) + 2| + 1) + 1) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(-3|x - 3| + 2)^2 - 1 = (2x - 2)/(-1x - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3|(1sin(1π(1(-5x + 1)^2 + 5(-5x + 1)) - 3) - 2) - 2| = 1(4((-1x - 2)/(2x))^2 - 2((-1x - 2)/(2x)) - 2) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(1π((-1(-5(-2x^2 - 2x - 5) + 2) + 3)/(-2(-5(-2x^2 - 2x - 5) + 2) - 1))) - 3 = -1|(-1((2x + 1)/(-1x - 1)) - 2) + 1| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1e^(1((-1(2(1|x| - 2) + 2))/(1(2(1|x| - 2) + 2) + 1))) and g(x) = 3|((1(-2x^2 + 4x - 4))/(-3(-2x^2 + 4x - 4) + 4)) - 3| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(-4((1(2|x + 2| - 3) - 2)/(-2(2|x + 2| - 3) - 3)) + 5)^2 - 2(-4((1(2|x + 2| - 3) - 2)/(-2(2|x + 2| - 3) - 3)) + 5) + 3 and g(x) = 2((-3(1|x + 3|) + 1)/(-1(1|x + 3|) + 3))^2 - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(-2|(-3cos(2π((1x + 3)/(3x + 3)) - 3) + 2) - 3| + 3)^2 - 4(-2|(-3cos(2π((1x + 3)/(3x + 3)) - 3) + 2) - 3| + 3) + 1 and g(x) = -3e^(-2(1|(2x^2 - 2) + 2| + 1)) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2sin(3π(1|(1x^2 - 4x - 2)|) - 1) - 2 and g(x) = -3|(5x^2 - 5x + 1) + 2| + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-3sin(3πx - 3)) - 3 = 3|x + 2| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(-3((3(-4x^2 + 3) + 3)/(1(-4x^2 + 3))) + 3) - 3| and g(x) = (3(2|(4x^2 + 1x - 5) + 2| - 3))/(1(2|(4x^2 + 1x - 5) + 2| - 3) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(2(-1|x| + 2) + 4) + 1)/(1(2(-1|x| + 2) + 4)) and g(x) = 2|(-2sin(2πx + 3) + 3) + 1| + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(2e^(1(3(1|x| - 2) - 5)) - 2) - 1)/(-2(2e^(1(3(1|x| - 2) - 5)) - 2) + 3) and g(x) = (1(-2(-1x)^2 - 4(-1x) - 2) + 3)/(-3(-2(-1x)^2 - 4(-1x) - 2) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5(-3x^2 + 4x) and g(x) = -1x^2 - 1x + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(-1sin(1π(4(4x^2 - 2x - 3) - 5) - 2) + 3) - 2| - 3 and g(x) = -2cos(3π(2(-4x^2) + 4) + 1) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3|(-2((2x + 1)/(-1x + 2))^2 - 2((2x + 1)/(-1x + 2)) + 3) + 3| - 1 and g(x) = -1(2|x + 3| + 1) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1((3x - 3)/(2x + 2))^2 + 2((3x - 3)/(2x + 2)) - 1 and g(x) = (1x + 3)/(-2x - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2sin(2π((-3(-1x^2 + 3x - 4) - 2)/(3(-1x^2 + 3x - 4) - 2)) - 3) - 1 and g(x) = 3(-3x^2 + 4x + 3) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(-2cos(3πx + 2) - 2) + 3)/(2(-2cos(3πx + 2) - 2) + 2) and g(x) = -5x^2 + 4x - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(3sin(3πx + 1)) - 2 and g(x) = -1|x + 2| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(-1x - 4)^2 - 5(-1x - 4) + 4 = 5x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(-5(-2sin(2π(1x^2 + 5x) + 3) + 2) + 3) - 2)/(2(-5(-2sin(2π(1x^2 + 5x) + 3) + 2) + 3) + 1) and g(x) = (1(3|(-3e^(2x) - 1) - 1| - 2) + 2)/(1(3|(-3e^(2x) - 1) - 1| - 2) - 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(-3|x + 3|)^2 - 3(-3|x + 3|) + 3 and g(x) = -3|x + 3| + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|(-3x - 2) - 3| + 3 and g(x) = 1x^2 + 5x - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2|(2sin(3π((-1x + 2)/(-2x - 1)) + 3)) - 2| - 2 and g(x) = 4(2cos(2πx + 3) - 3)^2 + 1(2cos(2πx + 3) - 3) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|((-2x - 3)/(-1x + 3)) + 1| = -2|x + 2| + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (2(1(2cos(1π(3|x + 2| - 3) - 2) - 2)^2 + 3(2cos(1π(3|x + 2| - 3) - 2) - 2) + 2) + 2)/(2(1(2cos(1π(3|x + 2| - 3) - 2) - 2)^2 + 3(2cos(1π(3|x + 2| - 3) - 2) - 2) + 2) + 3) and g(x) = 3sin(1π(-5(-2|x - 3| + 2)^2 - 4(-2|x - 3| + 2) - 3) + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3|(-4((1x + 1)/(2x + 1))^2 - 1((1x + 1)/(2x + 1)) - 2) + 2| and g(x) = (2(-3x + 5))/(1(-3x + 5) - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-3(-3x - 2) + 1)/(-1(-3x - 2) - 2) = 3|x + 3| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-2(3(-3|x - 3| + 3) + 4) - 2)/(1(3(-3|x - 3| + 3) + 4) - 2) and g(x) = -3((-1x - 3)/(-2x + 3))^2 + 1((-1x - 3)/(-2x + 3)) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1sin(2π(5(-2|((2x + 1)/(-3x + 2)) + 1| + 1)^2 - 4)) + 1 and g(x) = -2|(1((-3x + 3)/(-1x + 2))^2 - 4((-3x + 3)/(-1x + 2)) + 5) - 3| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(-3(-2sin(3πx + 2) - 1)^2 - 2(-2sin(3πx + 2) - 1) + 1) + 1| - 1 and g(x) = 1sin(2π(-1x + 2) + 2) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3e^(1(4((-2x)/(-2x + 3))^2 + 4((-2x)/(-2x + 3)) - 3)) + 2 and g(x) = 4((3x + 1)/(1x + 1)) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4((-3x + 3)/(-2x + 3))^2 - 1 and g(x) = -3x in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2(1cos(1π((-2x + 3)/(1x + 1))) + 3)^2 - 3(1cos(1π((-2x + 3)/(1x + 1))) + 3) - 1 = -2(1x - 5)^2 + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4((-2x + 1)/(-1x + 3))^2 - 4((-2x + 1)/(-1x + 3)) - 2 = -1x^2 - 2x - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3((2(1|(-3e^(1x) + 1) + 3|))/(1(1|(-3e^(1x) + 1) + 3|) + 2))^2 - 1((2(1|(-3e^(1x) + 1) + 3|))/(1(1|(-3e^(1x) + 1) + 3|) + 2)) = -1(2e^(1(5x^2 + 2x - 3)) - 3) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(2π(-1((-2x - 2)/(-1x + 2))^2 - 1((-2x - 2)/(-1x + 2)) + 5) + 3) + 2 and g(x) = -1|(-4x^2 - 3x + 2) + 2| + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3(-1|((-1(1e^(-2x) + 2) + 2)/(-2(1e^(-2x) + 2) - 2))|)^2 + 4(-1|((-1(1e^(-2x) + 2) + 2)/(-2(1e^(-2x) + 2) - 2))|) and g(x) = 3cos(2π((-3(4x^2 + 2x + 3) - 3)/(2(4x^2 + 2x + 3) - 1)) + 3) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(1|(5((2x + 1)/(-1x - 2)) + 1) - 3| + 1)^2 + 1(1|(5((2x + 1)/(-1x - 2)) + 1) - 3| + 1) - 3 = 1((2(2sin(3πx - 1) - 3) + 3)/(-1(2sin(3πx - 1) - 3) - 3))^2 + 5((2(2sin(3πx - 1) - 3) + 3)/(-1(2sin(3πx - 1) - 3) - 3)) - 3 have for x in the interval [-10, 10]?

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[User]
Find the number of times the graphs of f(x) = -3|(4x)| + 1 and g(x) = -3x intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(-3sin(3πx - 3) + 1) + 3 and g(x) = (1x + 1)/(2x) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(-2cos(3π((2(2|x + 1|) - 3)/(2(2|x + 1|))) + 1) + 2)^2 - 5(-2cos(3π((2(2|x + 1|) - 3)/(2(2|x + 1|))) + 1) + 2) - 1 and g(x) = (3(-3cos(1π(-3|x - 2|) + 1) + 3) - 3)/(3(-3cos(1π(-3|x - 2|) + 1) + 3) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(3|(-1(-3cos(2πx + 2) + 3)^2 + 4(-3cos(2πx + 2) + 3) + 3) - 1| + 1))/(-2(3|(-1(-3cos(2πx + 2) + 3)^2 + 4(-3cos(2πx + 2) + 3) + 3) - 1| + 1) - 2) and g(x) = -1|(3e^(-1((-3x + 1)/(3x + 1))) - 3) - 3| + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2sin(3π((-2x + 3)/(-1x - 3)) - 1) - 3 and g(x) = (-2x + 2)/(3x + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|((-2(1(5x^2 + 3x - 4) - 4) - 2)/(-1(1(5x^2 + 3x - 4) - 4) + 3)) + 1| - 3 and g(x) = -1|(-3sin(1π((2x - 1)/(1x - 3)) - 3)) - 2| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-3cos(1πx + 2) - 3) + 3)/(-2(-3cos(1πx + 2) - 3)) and g(x) = -1x^2 - 2x - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(-3|x - 1| - 1) + 4 and g(x) = 1x^2 - 2x + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4(3sin(1π(2(3|x - 3| + 2)^2 + 5(3|x - 3| + 2) - 1) + 1) + 3) + 5 and g(x) = -1cos(1π(-3|(-2x^2 + 5x - 1) + 3| - 2) - 3) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(1(-1cos(3π(3|x - 2| - 1) - 1) - 3) + 4) + 3)/(1(1(-1cos(3π(3|x - 2| - 1) - 1) - 3) + 4) + 3) and g(x) = 4(2((-2x - 2)/(2x)) - 1)^2 + 2(2((-2x - 2)/(2x)) - 1) - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(1cos(2πx - 3) + 1) - 3 and g(x) = -2x^2 - 1x intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1sin(2π((3x + 1)/(-3x)) - 2) - 3 = -5x^2 + 1x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1|(-2((-1(2x + 1) + 2)/(-2(2x + 1) - 1))^2 - 4((-1(2x + 1) + 2)/(-2(2x + 1) - 1)) - 3) + 3| and g(x) = 3|((2(-2sin(1πx + 1) - 2) - 1)/(1(-2sin(1πx + 1) - 2) - 3)) - 1| - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3|(2((-1(5x^2 - 5x + 2) - 1)/(-2(5x^2 - 5x + 2) + 1))) - 1| - 1 and g(x) = 3|(1cos(3π(1x + 1) - 3) + 1) + 3| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(5(2e^(2(-1x - 4)) - 3)^2 + 5(2e^(2(-1x - 4)) - 3) - 2) - 1)/(-3(5(2e^(2(-1x - 4)) - 3)^2 + 5(2e^(2(-1x - 4)) - 3) - 2)) = (1(-4(1cos(2πx - 1) + 2) + 3) + 3)/(2(-4(1cos(2πx - 1) + 2) + 3) + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(2|((-2x - 2)/(2x - 1)) + 1| - 3) and g(x) = (-1(2sin(3πx) + 1) - 3)/(-2(2sin(3πx) + 1) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1((1x + 1)/(-1x - 3))^2 - 3((1x + 1)/(-1x - 3)) + 5 = 3x^2 - 4x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1((2(-1|x + 2| + 1) + 1)/(1(-1|x + 2| + 1) - 3))^2 - 1((2(-1|x + 2| + 1) + 1)/(1(-1|x + 2| + 1) - 3)) - 3 and g(x) = -1(4x + 5)^2 + 1(4x + 5) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(1|(3e^(2x) - 1)| - 2) - 3)/(3(1|(3e^(2x) - 1)| - 2) + 2) = 1(-1x^2 + 5x + 3) - 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4((-3(3|x - 2| - 3) + 1)/(-2(3|x - 2| - 3) + 3))^2 + 2((-3(3|x - 2| - 3) + 1)/(-2(3|x - 2| - 3) + 3)) - 1 and g(x) = -5(1e^(1x))^2 + 3(1e^(1x)) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1sin(1π(-2|x + 1| + 2) - 3) and g(x) = 2x^2 - 2x - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(2π((-1(1|(5x - 1) - 2| - 3) + 1)/(3(1|(5x - 1) - 2| - 3) - 2)) - 3) - 2 and g(x) = (-3(-2|(1x - 5) + 3| + 2) + 3)/(1(-2|(1x - 5) + 3| + 2) - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(-5(-2|x + 2| - 2) + 2) - 1)/(2(-5(-2|x + 2| - 2) + 2)) and g(x) = (-2(-2cos(3πx + 3) + 1) + 2)/(-3(-2cos(3πx + 3) + 1)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3|(-2cos(2π(2x) + 1) - 3) + 2| + 2 and g(x) = 5(3x)^2 - 2(3x) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1|(5(2e^(1((-3x - 2)/(1x + 1))) + 2)) - 3| + 2 and g(x) = 2e^(2(-5(3|x - 3| - 2) - 4)) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3cos(1π((3(-1x + 5) + 3)/(3(-1x + 5) - 2)) - 2) - 3 = -3sin(2π((2x - 2)/(-3x + 2))) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -4((2(-5x + 2) + 1)/(-1(-5x + 2) - 1))^2 + 5((2(-5x + 2) + 1)/(-1(-5x + 2) - 1)) - 2 = -3((-2x + 1)/(-1x + 3)) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1|((3(-3(-1sin(1πx)) - 2) - 2)/(1(-3(-1sin(1πx)) - 2) + 3)) + 2| + 2 and g(x) = 2(1(-3sin(3πx - 2) + 1) - 3)^2 - 5(1(-3sin(3πx - 2) + 1) - 3) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(2(-3(-1|x + 3|) - 1)^2 - 1(-3(-1|x + 3|) - 1) - 4) - 1)/(3(2(-3(-1|x + 3|) - 1)^2 - 1(-3(-1|x + 3|) - 1) - 4) - 2) and g(x) = -4((1(1x + 3) + 2)/(2(1x + 3)))^2 - 4((1(1x + 3) + 2)/(2(1x + 3))) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(-1(-2|((-2x + 2)/(-2x)) - 2| + 2)^2 + 2(-2|((-2x + 2)/(-2x)) - 2| + 2) - 2) + 5 and g(x) = -1cos(2π(2((-3x - 1)/(-3x - 3)) + 5)) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|(-5(2((3x)/(-1x + 2))^2) + 1) + 3| - 1 and g(x) = -4((1(-2x + 4) - 1)/(3(-2x + 4) + 2))^2 + 1((1(-2x + 4) - 1)/(3(-2x + 4) + 2)) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2((2x - 3)/(3x + 1))^2 - 1((2x - 3)/(3x + 1)) - 5 = -2|x + 3| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(5(-4x - 1)^2 + 2(-4x - 1)) - 2)/(2(5(-4x - 1)^2 + 2(-4x - 1)) - 1) and g(x) = 4(-1sin(3πx)) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2sin(3π(-3(-5x^2 + 2x + 5) - 1) + 2) - 2 and g(x) = -1e^(-2(-5x)) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4((-1(1|(-2sin(1πx)) + 2| - 2) + 1)/(1(1|(-2sin(1πx)) + 2| - 2) + 1)) and g(x) = (-2(-1sin(1π(-2x - 2) - 1) + 2))/(1(-1sin(1π(-2x - 2) - 1) + 2)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2(5x + 5)^2 - 3(5x + 5) and g(x) = 3|x + 1| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(-1sin(2πx - 1) + 3))/(3(-1sin(2πx - 1) + 3) + 2) = -3|x + 2| + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5(-2cos(1πx + 1) - 2)^2 + 5(-2cos(1πx + 1) - 2) + 1 and g(x) = -2x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(2|x - 3| + 3) - 1 and g(x) = 3|x + 1| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(-4((-3(5x^2 - 2x + 4) - 3)/(3(5x^2 - 2x + 4))) - 4) + 2| - 3 and g(x) = (1(-1(3sin(2πx - 3) + 3) + 3) - 3)/(-1(-1(3sin(2πx - 3) + 3) + 3) - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(2|(-1(-4x^2 + 1) - 4) - 3| + 3) + 2)/(1(2|(-1(-4x^2 + 1) - 4) - 3| + 3) - 3) and g(x) = 1|((-3(3e^(1x) - 3) + 3)/(-3(3e^(1x) - 3) - 2)) + 2| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2(1cos(2π(1|x| + 1) + 1) - 3)^2 - 3(1cos(2π(1|x| + 1) + 1) - 3) + 4 and g(x) = 3|(-1x^2 + 1x) - 2| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(2e^(-2x)) + 2)/(-3(2e^(-2x))) and g(x) = (-2x - 1)/(3x) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(2sin(2πx + 3) + 2) - 3 and g(x) = 1x + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(2sin(3π((-1(-1x^2 - 2x - 5) - 3)/(-2(-1x^2 - 2x - 5) - 3))) + 3) - 1 and g(x) = (1(-2(-1x - 1)^2 + 4(-1x - 1) + 5) + 1)/(1(-2(-1x - 1)^2 + 4(-1x - 1) + 5) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(-2((1x - 1)/(1x + 3)) - 5)^2 + 4(-2((1x - 1)/(1x + 3)) - 5) + 2 and g(x) = (1(1e^(-1x) + 2) - 3)/(1(1e^(-1x) + 2) + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2cos(3π((2x + 1)/(-3x))) - 1 and g(x) = -2x^2 + 2x + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1((-2(-1(-2sin(1πx - 2) + 2) + 4))/(-1(-1(-2sin(1πx - 2) + 2) + 4)))^2 - 1((-2(-1(-2sin(1πx - 2) + 2) + 4))/(-1(-1(-2sin(1πx - 2) + 2) + 4))) and g(x) = -2((-2(2cos(3πx - 3) - 2) - 1)/(-1(2cos(3πx - 3) - 2) - 2))^2 - 3((-2(2cos(3πx - 3) - 2) - 1)/(-1(2cos(3πx - 3) - 2) - 2)) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(-1cos(2πx - 1) - 3) - 3 and g(x) = 1x - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(3π((1(-3x - 3) + 3)/(-2(-3x - 3) - 2)) - 2) + 1 and g(x) = (2(-2|x - 1| - 1) + 3)/(3(-2|x - 1| - 1) + 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2((2(-1|(1x^2 + 5x + 4) - 3| - 2) + 1)/(1(-1|(1x^2 + 5x + 4) - 3| - 2) + 3)) = (1(5(-3|x - 2| + 2)^2 - 4(-3|x - 2| + 2) - 5) - 3)/(1(5(-3|x - 2| + 2)^2 - 4(-3|x - 2| + 2) - 5)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(1(1|x + 3| - 1)^2 + 1(1|x + 3| - 1) - 3) - 5 and g(x) = -1cos(1π(3|x - 2|) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(5(2x - 2)^2 + 1(2x - 2)))/(2(5(2x - 2)^2 + 1(2x - 2)) - 3) and g(x) = -1sin(3π(-2x^2 - 2x - 1) + 3) + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4((1(-1sin(3π(1|x + 1| + 3) - 1) - 2) - 3)/(-2(-1sin(3π(1|x + 1| + 3) - 1) - 2)))^2 + 4((1(-1sin(3π(1|x + 1| + 3) - 1) - 2) - 3)/(-2(-1sin(3π(1|x + 1| + 3) - 1) - 2))) - 1 and g(x) = -2((2(-2|x + 3| + 2) + 1)/(2(-2|x + 3| + 2) - 1))^2 + 4((2(-2|x + 3| + 2) + 1)/(2(-2|x + 3| + 2) - 1)) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5((-1(-1(-1|x| + 3) - 4) - 3)/(3(-1(-1|x| + 3) - 4) + 3))^2 - 1 and g(x) = 1cos(1π((-1(5x + 5) + 1)/(-2(5x + 5) + 3)) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4((2(2e^(2x) - 2) - 2)/(-3(2e^(2x) - 2) + 2))^2 + 4 and g(x) = (2(3cos(2πx + 2) + 2) - 2)/(-3(3cos(2πx + 2) + 2) - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(3cos(2πx + 3) + 3) + 2 and g(x) = -1x^2 - 1x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2|(1cos(3π(-1x) + 3) + 1) + 1| - 2 and g(x) = (-2(1x) + 2)/(1(1x) - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5(-1e^(2x) + 1)^2 - 3 and g(x) = -1x^2 - 4x - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(1cos(1π(3x - 1)) - 1) + 3)/(3(1cos(1π(3x - 1)) - 1) + 2) and g(x) = 2(2cos(3πx + 2) - 1)^2 - 4(2cos(3πx + 2) - 1) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(5(2|x + 3| + 2) - 3)^2 + 3(5(2|x + 3| + 2) - 3) + 3 and g(x) = 3e^(-1(-3x^2 - 3x + 4)) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4((2(-2cos(2πx) - 1))/(3(-2cos(2πx) - 1) - 2)) + 1 and g(x) = -3|(1cos(1πx) + 1) + 3| - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(-5(5(2cos(3πx) - 1)^2 - 3(2cos(3πx) - 1) + 3) + 5) - 3| - 1 and g(x) = -2(-3e^(-1((3x - 2)/(-3x + 2))) + 3)^2 + 3(-3e^(-1((3x - 2)/(-3x + 2))) + 3) - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(-3(-2|x - 3| + 3)^2 + 4(-2|x - 3| + 3) + 1) - 1 and g(x) = (3(-1sin(3πx) - 3) + 2)/(3(-1sin(3πx) - 3) + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|((2(-4(-2x^2 - 3x + 3) - 3) - 2)/(3(-4(-2x^2 - 3x + 3) - 3) + 1)) + 2| + 2 = 1cos(1π(1((-1x - 3)/(3x + 2)) + 2) + 2) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(1|((3(2x^2 - 2x - 5))/(2(2x^2 - 2x - 5) - 1)) - 1| - 3) + 4 and g(x) = (2(-1(1|x| - 3) + 3) - 3)/(2(-1(1|x| - 3) + 3) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(1(1|((-2x - 1)/(1x + 3))| - 2)^2 + 1(1|((-2x - 1)/(1x + 3))| - 2) - 1) + 5 and g(x) = (-1(-2|(5x + 5) - 1| + 2) + 1)/(-3(-2|(5x + 5) - 1| + 2) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-3|x - 2| - 1) + 1 = -3|x - 1| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3|((1(3x + 4) - 2)/(3(3x + 4) - 2)) + 2| - 2 and g(x) = -1(2cos(3πx + 3) + 3)^2 + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3sin(1π(-1(4(1|x + 1| - 1)^2 + 3(1|x + 1| - 1) - 2) + 3) - 3) = 2(5((-2x + 3)/(1x + 3))^2 - 5((-2x + 3)/(1x + 3)) - 2) + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(-4(-1sin(3πx)) - 2) + 2| + 1 and g(x) = (1(1|x - 3| + 2) - 3)/(2(1|x - 3| + 2) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4(-2e^(2(-3x^2 + 4x - 3)) + 3) + 2 = 1(2|x| - 2) + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(2(-3cos(3π((-2x + 3)/(2x - 3))) + 3)^2 + 1(-3cos(3π((-2x + 3)/(2x - 3))) + 3) - 4) + 1 and g(x) = 3(-1|((-3x + 1)/(-2x)) + 2| + 3) - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|((3(-3(2x)^2 - 5(2x) + 5) + 2)/(-1(-3(2x)^2 - 5(2x) + 5) + 3)) + 2| - 1 and g(x) = (-2(-4(1x^2 - 3) - 3))/(-2(-4(1x^2 - 3) - 3) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(-1(-4x^2 - 5x) - 4) + 3| - 1 and g(x) = -2|(5x^2 + 5x - 5)| + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(3(3(3|x - 2| + 2)^2 + 1(3|x - 2| + 2) + 1) + 2) - 2)/(3(3(3(3|x - 2| + 2)^2 + 1(3|x - 2| + 2) + 1) + 2) + 3) and g(x) = (1(2|(1x - 4) - 1| + 3) - 3)/(2(2|(1x - 4) - 1| + 3) + 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(1(-3(3|x - 1| - 3)^2 + 4(3|x - 1| - 3) + 2) + 3) + 1)/(-3(1(-3(3|x - 1| - 3)^2 + 4(3|x - 1| - 3) + 2) + 3) + 4) and g(x) = 1cos(2π(-2(3|x| - 1)^2 + 2(3|x| - 1))) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2e^(-1(-1(-2|((3x - 1)/(-1x + 2)) + 2| + 1) - 2)) - 3 = -3|(5(-4x^2 + 4x - 1)) + 1| + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(1((3x - 3)/(3x - 2)) + 1) - 2| + 3 = -2cos(1π(-1x^2 + 2x) + 2) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(-1sin(2πx) - 3) + 2| - 3 and g(x) = -1|x - 1| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2e^(2(-4((-1(-1|x - 3| + 3) - 3)/(1(-1|x - 3| + 3)))^2 + 1((-1(-1|x - 3| + 3) - 3)/(1(-1|x - 3| + 3))) + 4)) + 1 and g(x) = -3cos(2π((-2(-2x + 2) + 2)/(2(-2x + 2) - 1)) - 1) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1|((2(2(-1x^2 + 4x + 2) - 3) - 1)/(2(2(-1x^2 + 4x + 2) - 3))) - 2| + 3 = (-1(1(-5x + 4)^2 + 1(-5x + 4) - 1) + 1)/(-1(1(-5x + 4)^2 + 1(-5x + 4) - 1) - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|(-1(1x^2 - 2x + 1) + 3) + 3| + 2 = -2sin(1π((2x + 1)/(1x)) + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3|(-2(-1((-1x - 3)/(3x - 1)) + 1)^2 + 1) + 2| + 1 = 2(-1|((-3x + 3)/(-1x - 1)) + 1| + 1)^2 - 3(-1|((-3x + 3)/(-1x - 1)) + 1| + 1) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1cos(2π(3|(-4x^2 + 1x - 2) - 3| + 1) + 3) + 2 = -3(2x - 4)^2 + 3(2x - 4) + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(2π(1|((2x - 3)/(2x)) + 3| + 3) - 1) - 1 and g(x) = -3sin(3π(-3|x| - 2) - 3) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(1e^(2x) - 2) - 3| - 2 = -2x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1((-3(-2|x - 3| + 3) - 3)/(-1(-2|x - 3| + 3) + 3)) and g(x) = 4(-2x + 3)^2 + 4(-2x + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(2|x - 3| - 1) - 3)/(1(2|x - 3| - 1) - 3) and g(x) = (-3x + 1)/(-2x - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3((-1(3cos(3π(3|x + 1| - 2) + 2) - 1))/(-1(3cos(3π(3|x + 1| - 2) + 2) - 1) - 3)) - 4 = -1((-2(-2|x + 2| + 3) + 3)/(2(-2|x + 2| + 3) + 1))^2 + 5((-2(-2|x + 2| + 3) + 3)/(2(-2|x + 2| + 3) + 1)) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3|((1(-3e^(-1x) + 3) + 2)/(3(-3e^(-1x) + 3) + 1)) - 2| + 2 and g(x) = 3sin(1π(4x^2 - 5x) - 2) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(3sin(2π(2(-5x + 4)^2 + 3(-5x + 4) + 1) - 1) + 3) - 3)/(2(3sin(2π(2(-5x + 4)^2 + 3(-5x + 4) + 1) - 1) + 3) - 1) and g(x) = 2sin(3π(-2(3|x + 2| - 3)^2 - 2(3|x + 2| - 3))) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1e^(1((-2(1|(-5x^2 + 2x - 4) + 2| - 3) + 1)/(2(1|(-5x^2 + 2x - 4) + 2| - 3) + 1))) + 1 and g(x) = -5(3((-2x - 2)/(1x + 3)) - 4)^2 - 5(3((-2x - 2)/(1x + 3)) - 4) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(1sin(3πx - 1) - 3) + 2)/(-1(1sin(3πx - 1) - 3) - 1) = -3x - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(2|(1x + 5)| - 1) + 3)/(1(2|(1x + 5)| - 1) - 2) and g(x) = -3sin(1π(-3|x - 2| - 2) + 1) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1((-2(-3|(1x + 2) - 3| + 1))/(-2(-3|(1x + 2) - 3| + 1) + 1))^2 - 3((-2(-3|(1x + 2) - 3| + 1))/(-2(-3|(1x + 2) - 3| + 1) + 1)) - 4 and g(x) = -1((-2(-2sin(3πx - 1) + 2) - 3)/(-1(-2sin(3πx - 1) + 2) + 2))^2 - 5((-2(-2sin(3πx - 1) + 2) - 3)/(-1(-2sin(3πx - 1) + 2) + 2)) + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5((-1x - 3)/(-2x + 1)) - 5 and g(x) = (-1x - 1)/(1x + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2((1(-3|(-4x^2 + 2) - 2| + 2) - 2)/(3(-3|(-4x^2 + 2) - 2| + 2) - 2)) - 1 and g(x) = (-2(3(-2x^2 + 4x - 4) - 1))/(1(3(-2x^2 + 4x - 4) - 1) + 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(3π(-3|((-2x + 3)/(-1x - 1)) - 3|) + 3) - 1 = 1((-3x)/(3x - 1))^2 + 1((-3x)/(3x - 1)) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(3π((1(-3|x - 1| - 1) - 1)/(2(-3|x - 1| - 1) + 1)) - 3) - 3 = -1sin(3π(4x^2 + 5x + 1) + 3) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(-3|(2((-2x)/(1x - 3))^2 + 3((-2x)/(1x - 3)) + 4) - 2| + 3) + 3 and g(x) = 1(2cos(2π(-5x - 3) - 3))^2 - 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(-4x + 5) + 1)/(-3(-4x + 5)) and g(x) = 3|x + 2| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3((-3(3|x + 1| - 3))/(-2(3|x + 1| - 3) - 2)) - 1 and g(x) = -3(-1x^2 + 4x + 4) - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (3(3(2x^2 + 2x + 4)) + 2)/(3(3(2x^2 + 2x + 4))) and g(x) = 5(1|x| - 2)^2 - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(1(5x - 1)^2 + 5(5x - 1)) + 2)/(2(1(5x - 1)^2 + 5(5x - 1))) = 2|(-2x)| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3|(-5(-2cos(3π(2x^2 + 2x + 5) - 2) + 1) - 1) - 2| - 3 and g(x) = 2cos(3π((2(-5x^2 + 5x) - 3)/(3(-5x^2 + 5x)))) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(-1|(5x^2 + 1x - 2) - 2|) - 2)/(-1(-1|(5x^2 + 1x - 2) - 2|) - 2) and g(x) = -4((-2x - 2)/(-1x - 2)) - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(3|x + 2|) + 2 = 5x^2 - 1x - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3|(1(3x - 2)^2 - 1(3x - 2) - 5) + 1| - 1 = -2(3|x + 1| - 3) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(1e^(-1x) - 3) - 1)/(2(1e^(-1x) - 3)) and g(x) = 1x in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5(-1((3x - 1)/(-3x - 2)) + 1)^2 + 4(-1((3x - 1)/(-3x - 2)) + 1) + 1 and g(x) = 3|(-4x^2 + 1x - 3) + 2| - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3e^(-1(-2x^2 + 3x + 4)) - 3 and g(x) = (1x - 3)/(3x - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(2|x - 1| + 2) - 4 and g(x) = 1x^2 + 2x - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(4(-1|((-3x - 3)/(1x + 3)) - 2| + 1) + 3)^2 - 4(4(-1|((-3x - 3)/(1x + 3)) - 2| + 1) + 3) + 2 and g(x) = -1(-2sin(2π(-1x^2 + 1x - 2) - 2) - 3) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4((1(-1|(-4x + 5)| - 1) - 3)/(3(-1|(-4x + 5)| - 1) - 2))^2 and g(x) = -2(3((-3x + 2)/(2x - 1)) + 2)^2 - 3(3((-3x + 2)/(2x - 1)) + 2) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(-1(1|(3e^(1x) - 3) + 2| + 3)))/(3(-1(1|(3e^(1x) - 3) + 2| + 3)) - 1) and g(x) = (3(3|(-2x^2 - 4x + 5)| - 1) - 3)/(1(3|(-2x^2 - 4x + 5)| - 1)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(-3(-2sin(3π(3x^2 + 3x)) + 3) + 2) + 1)/(-3(-3(-2sin(3π(3x^2 + 3x)) + 3) + 2) - 2) = 1e^(-2((2(2x^2 - 4x - 1))/(-2(2x^2 - 4x - 1) - 1))) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2((-3x + 1)/(1x))^2 + 1((-3x + 1)/(1x)) - 2 and g(x) = -5x^2 - 2x + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3|(3((2x)/(-3x - 3)) + 3) - 3| - 2 and g(x) = -3(-3x^2 - 1x + 4) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(4x^2 - 2x - 4) - 1)/(-1(4x^2 - 2x - 4) - 1) and g(x) = -3|x| + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(2sin(1πx + 2)) - 2)/(1(2sin(1πx + 2)) + 3) = -5x^2 + 4x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1sin(1π(1x^2 + 4x - 3) - 2) - 3 = -1x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(-3(2|(1x - 2) - 1| - 2)^2 - 1(2|(1x - 2) - 1| - 2) + 3) + 2)/(-1(-3(2|(1x - 2) - 1| - 2)^2 - 1(2|(1x - 2) - 1| - 2) + 3) + 3) and g(x) = -2|(5((-3x - 3)/(-3x + 1)) + 3) - 1| - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(1(3|((-2x - 2)/(3x + 3)) - 1| - 1)^2 + 5(3|((-2x - 2)/(3x + 3)) - 1| - 1) + 1) - 3 and g(x) = -4((-3(2|x| - 1))/(-1(2|x| - 1) + 3)) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3(3x^2 - 5) - 3 and g(x) = -3|x + 2| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4(-2cos(2π(-2|x|) + 3) + 2) + 4 and g(x) = (-2(-3cos(1πx)) + 1)/(1(-3cos(1πx)) - 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4(-2x^2 - 5x + 5) - 2 and g(x) = (-2x + 1)/(1x - 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(-2(3(2|x + 1| + 2) + 2)^2 - 4(3(2|x + 1| + 2) + 2) - 5) - 3)/(1(-2(3(2|x + 1| + 2) + 2)^2 - 4(3(2|x + 1| + 2) + 2) - 5) + 2) and g(x) = 3|(1(-2cos(3πx + 2) - 3) + 1) - 1| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(3x + 2)^2 - 3(3x + 2) + 5 and g(x) = -3x^2 - 1x + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|(1x^2 + 3x - 5) - 2| - 3 and g(x) = 2x - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(3(2sin(1π(-3|x + 1| - 1) - 1))^2 + 1(2sin(1π(-3|x + 1| - 1) - 1)) - 3) + 2 and g(x) = 1((2(2|x - 3| + 3) + 2)/(1(2|x - 3| + 3))) + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(-2(-4x - 1)^2 + 1(-4x - 1) + 3) + 1)/(2(-2(-4x - 1)^2 + 1(-4x - 1) + 3) + 1) and g(x) = 2|(-3x^2 - 4x + 1) - 3| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(2(-1cos(3πx - 3) + 2)^2 + 4(-1cos(3πx - 3) + 2) - 3) - 3| + 3 and g(x) = 2e^(2(1x)) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(-2(1|(-1cos(2πx) - 3) + 3| - 1) + 3)^2 + 3(-2(1|(-1cos(2πx) - 3) + 3| - 1) + 3) - 4 = 2(-3((2x + 2)/(-1x - 3))^2 - 2((2x + 2)/(-1x - 3)) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2(-1|(-2sin(1πx) - 3) + 2| + 3)^2 - 3(-1|(-2sin(1πx) - 3) + 2| + 3) - 5 and g(x) = -1(2sin(1πx + 1)) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(2cos(2πx + 3) + 2) - 1| + 2 and g(x) = (-3x)/(-2x + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(2cos(3π(2x^2 + 1x) + 3) - 1) + 3)/(-3(2cos(3π(2x^2 + 1x) + 3) - 1)) = -5(3cos(2πx - 3) - 2) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1|((2(-1x^2 - 3x + 2) - 3)/(-1(-1x^2 - 3x + 2) + 3)) - 1| - 3 and g(x) = (-3(1x - 5) + 3)/(-3(1x - 5) - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3((2(3x - 5) + 2)/(1(3x - 5) + 3))^2 - 4((2(3x - 5) + 2)/(1(3x - 5) + 3)) + 3 and g(x) = -1|((-2x - 2)/(1x - 2)) + 1| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(5(-2|x| + 1) + 1) + 2)/(-2(5(-2|x| + 1) + 1) - 2) and g(x) = 2cos(3π(5x^2 + 3) + 3) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4(3cos(3πx + 3) + 3) + 4 = 1|x + 1| - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(-1sin(2π(1|x - 3| + 2) - 3) - 1) - 4 and g(x) = (1(1x^2 - 4x - 2) - 2)/(3(1x^2 - 4x - 2) + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|((-2(1sin(2πx) - 1))/(-1(1sin(2πx) - 1) - 2)) + 1| and g(x) = (-2(-1x^2 + 5x - 4) + 1)/(-1(-1x^2 + 5x - 4) + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(-3sin(1πx + 3)) - 4 = -4x^2 + 2x - 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1e^(1(-2|x + 2| + 3)) + 2 = 1x^2 - 2x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1|((1x + 2)/(-3x - 1)) - 1| + 3 and g(x) = 2x^2 + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3|(1sin(2π(-1(1x^2 - 4x - 1) + 4) - 1) - 2) - 1| + 3 and g(x) = -3(-5((2x + 2)/(-3x + 4)) - 1)^2 + 4(-5((2x + 2)/(-3x + 4)) - 1) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(2sin(1π((-3x + 3)/(-2x - 3)) + 3) + 2)^2 + 3(2sin(1π((-3x + 3)/(-2x - 3)) + 3) + 2) + 4 = 3|(-1e^(-1x) + 3) + 3| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(-2|(2(1x^2 - 2x - 5) + 1) + 2| - 2) - 2)/(2(-2|(2(1x^2 - 2x - 5) + 1) + 2| - 2) + 2) and g(x) = -1|(1cos(2π((1x + 1)/(-3x - 2)) + 2) - 1) - 2| + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1e^(-1(1|(-5x - 1)| + 3)) - 1 and g(x) = (-3(1|x + 3| - 1) + 3)/(1(1|x + 3| - 1)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5(-2sin(1πx - 2)) + 2 and g(x) = (-3x - 3)/(1x - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(-4((-2(1|x + 1|) + 3)/(1(1|x + 1|))) + 4)^2 - 3(-4((-2(1|x + 1|) + 3)/(1(1|x + 1|))) + 4) - 3 = 4(2((-1x - 3)/(-2x - 3))^2 - 5((-1x - 3)/(-2x - 3)) - 2) + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(2|x + 1| - 2))/(3(2|x + 1| - 2) + 1) = (2x)/(2x - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(-4((-2(1cos(2πx + 1)) + 1)/(2(1cos(2πx + 1)) - 1))^2 + 4((-2(1cos(2πx + 1)) + 1)/(2(1cos(2πx + 1)) - 1)) + 3) and g(x) = (1(5(2sin(1πx + 1))) + 1)/(2(5(2sin(1πx + 1))) - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(-2sin(3πx - 3) - 3)^2 - 3(-2sin(3πx - 3) - 3) + 5 and g(x) = -3|x + 3| - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(1π((3(2|(-1x^2 - 5x - 1) + 3| - 3) - 1)/(-1(2|(-1x^2 - 5x - 1) + 3| - 3) + 2)) + 3) - 1 and g(x) = 1(2e^(-1(4x^2 + 1x)) + 1) - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(2π(1|x - 1| - 3) + 3) + 3 = -1x + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|(2(1((-1x)/(-1x + 2))^2 + 2((-1x)/(-1x + 2)) + 1) - 2) + 1| = -2((-3(-5x^2 + 3x - 2) + 2)/(2(-5x^2 + 3x - 2))) - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3((3(-3|x - 1| + 3) + 3)/(3(-3|x - 1| + 3) + 1)) - 2 and g(x) = -3(1cos(3πx + 2)) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(4(1cos(1π((1x - 1)/(-3x + 2)) - 1) + 2)^2 + 3(1cos(1π((1x - 1)/(-3x + 2)) - 1) + 2) + 2) - 5 and g(x) = -1(-2|((2x)/(3x + 2)) - 1| - 2)^2 - 2(-2|((2x)/(3x + 2)) - 1| - 2) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4((1(-3sin(1πx - 2) + 1) - 1)/(-2(-3sin(1πx - 2) + 1)))^2 + 1((1(-3sin(1πx - 2) + 1) - 1)/(-2(-3sin(1πx - 2) + 1))) + 5 and g(x) = (-1(5x^2 - 5x - 5) + 2)/(-2(5x^2 - 5x - 5) - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-3(2(-1sin(1πx + 3) - 1) + 2) - 1)/(2(2(-1sin(1πx + 3) - 1) + 2) - 1) = (-1(-1e^(-1x) - 3))/(3(-1e^(-1x) - 3) - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1|(-3((1x - 1)/(-2x + 1))^2 - 2((1x - 1)/(-2x + 1)) - 4) + 2| + 1 = -1(3|x| - 1)^2 + 5(3|x| - 1) + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3((-3(-1|(-4x^2 + 2x - 2)| - 2) + 2)/(2(-1|(-4x^2 + 2x - 2)| - 2) + 1)) + 1 and g(x) = -3cos(3π(2|(2x + 1) - 2| - 3)) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(-3|((1(-1x + 2) + 1)/(3(-1x + 2) + 1)) + 1| - 3)^2 + 1(-3|((1(-1x + 2) + 1)/(3(-1x + 2) + 1)) + 1| - 3) + 3 and g(x) = -4(3|(-3e^(-2x) + 3) + 2| + 3) - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(1π(3x + 3) - 3) + 1 = 3|x + 3| + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(-1sin(2πx) - 2) - 2| - 1 and g(x) = 4x + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(-3((3x - 3)/(-3x + 1))^2 - 4((3x - 3)/(-3x + 1)) - 4) - 5 and g(x) = -1|((-2x - 2)/(2x + 1)) + 3| + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(2e^(2x) - 3))/(1(2e^(2x) - 3)) and g(x) = 1x^2 + 3x - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(-4((-2x + 3)/(2x))^2 - 5((-2x + 3)/(2x)) + 4) + 1| + 1 and g(x) = 3((-1x + 1)/(3x + 1))^2 + 2((-1x + 1)/(3x + 1)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(1(-3x^2 + 2x + 4) - 1) + 1)/(-2(1(-3x^2 + 2x + 4) - 1) + 3) and g(x) = 4(2sin(1πx + 2) - 3) - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1|(-1e^(-1(4(1x - 1)^2 + 3(1x - 1) + 1)) + 3) + 2| and g(x) = 1((-3(3x^2 + 1x - 3) + 1)/(1(3x^2 + 1x - 3) + 3)) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|((1x - 1)/(3x + 3)) - 3| + 3 and g(x) = 4x^2 - 5x - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3(-2sin(2π(3x^2 + 1x)) + 1) + 2 and g(x) = 2sin(3π((1x + 3)/(1x + 3)) - 3) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(2π(-1|x| + 1) + 1) = (-1x + 2)/(-1x + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(-1e^(2x) + 2)^2 - 1(-1e^(2x) + 2) + 2 and g(x) = -1|x + 3| in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1((-1(-4x - 5) - 2)/(1(-4x - 5) + 3))^2 + 3((-1(-4x - 5) - 2)/(1(-4x - 5) + 3)) - 5 and g(x) = 2|(-5x - 5) + 3| + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (2(3|(4x - 3)| - 3) + 2)/(3(3|(4x - 3)| - 3) + 1) and g(x) = (-1(5x - 2) + 3)/(-2(5x - 2) - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(-3sin(2πx + 3) + 1) - 3| - 1 = 4x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|(2cos(2π((-1(2x - 1))/(1(2x - 1) - 2)) - 1) + 1) + 3| = -5((1(-1|x + 3| + 1))/(2(-1|x + 3| + 1) + 2)) + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-1(-3|(2x^2 + 1x + 2) + 2| - 1) - 5) - 3)/(-3(-1(-3|(2x^2 + 1x + 2) + 2| - 1) - 5) - 1) and g(x) = -3(2((1x + 3)/(-3x - 1))^2 - 1((1x + 3)/(-3x - 1)) - 5) - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4(-1|((1(-3x^2 + 3x - 4) + 3)/(2(-3x^2 + 3x - 4) - 1)) + 3|) + 5 and g(x) = (1(-5(2|x + 2| - 2) + 1) + 3)/(1(-5(2|x + 2| - 2) + 1) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(3e^(1(-3|((-1x + 2)/(-1x)) - 1| - 2)) - 2) and g(x) = (-1(2(-1x^2 + 3x + 3) - 4))/(2(2(-1x^2 + 3x + 3) - 4) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5(-2sin(2π(-1|x + 1| - 3) - 3) - 1) - 3 and g(x) = 3sin(1π(-3x - 2) - 1) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(2π(1(-4(-3|x + 3| + 2) - 4)^2 + 5(-4(-3|x + 3| + 2) - 4) - 2) - 1) and g(x) = -2sin(2π((-1(1|x - 2| - 2) + 2)/(-3(1|x - 2| - 2) - 2)) + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|(4(2sin(3π(-5x - 1) + 3) + 2)^2 - 3) + 2| - 2 = (2(2(-3sin(3πx - 2)) - 2) - 3)/(-1(2(-3sin(3πx - 2)) - 2) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4((1(2(3|x| + 2)^2 - 5(3|x| + 2) + 1) + 3)/(1(2(3|x| + 2)^2 - 5(3|x| + 2) + 1))) + 4 and g(x) = -1e^(2(5(3|x| - 1)^2 - 3(3|x| - 1) - 1)) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(-2(3|(-1x + 5)| + 1)^2 + 3(3|(-1x + 5)| + 1) + 5) + 2)/(-1(-2(3|(-1x + 5)| + 1)^2 + 3(3|(-1x + 5)| + 1) + 5) + 2) and g(x) = -2cos(2π((3(1|x - 3| + 2) - 1)/(-1(1|x - 3| + 2) - 3)) - 2) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1cos(1π(3|x - 3| + 3) - 1) + 3 and g(x) = (-3x - 1)/(-2x - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(-3(1|(-5x^2 - 1x - 4) + 1|) + 1) - 2)/(-2(-3(1|(-5x^2 - 1x - 4) + 1|) + 1) - 2) = 5(2sin(3π((-3x - 1)/(2x)) + 1)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(3|x - 1| - 1))/(3(3|x - 1| - 1) + 3) and g(x) = -2|x - 3| where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(1(1(1|x + 2| - 2) - 2)^2 + 2(1(1|x + 2| - 2) - 2) + 1))/(-1(1(1(1|x + 2| - 2) - 2)^2 + 2(1(1|x + 2| - 2) - 2) + 1) + 2) and g(x) = (-3(3e^(-2(2|x| - 2))) + 2)/(1(3e^(-2(2|x| - 2))) - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(-3((3x - 3)/(-2x - 2)) - 1)^2 - 5(-3((3x - 3)/(-2x - 2)) - 1) + 1 and g(x) = 4(-3x + 5)^2 - 2(-3x + 5) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2sin(3π(-4(-1|(5x - 1) + 2| - 1)^2 + 4(-1|(5x - 1) + 2| - 1) + 3) + 1) - 2 and g(x) = -5(1|((-1x + 2)/(2x + 2)) - 3| - 1)^2 + 1(1|((-1x + 2)/(2x + 2)) - 3| - 1) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2((-2(-2|x - 2| - 1) + 1)/(2(-2|x - 2| - 1) - 1)) - 2 and g(x) = (2(-1|x + 1| + 1) - 1)/(1(-1|x + 1| + 1)) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(3cos(3π(-2x^2 + 2) - 2) - 3) + 1 and g(x) = -1|(3sin(2πx + 1) + 1) - 1| in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(3|(-3(-2x^2 - 5x - 2) - 5) + 3| + 1) + 3)/(-3(3|(-3(-2x^2 - 5x - 2) - 5) + 3| + 1) + 1) = 3sin(2π(4(-5x^2 - 1x - 2) - 4) - 2) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-1cos(3πx - 1) - 1) + 1)/(-1(-1cos(3πx - 1) - 1) + 2) and g(x) = -2|x + 1| + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1sin(1π(-3(1|x - 1|) + 3) + 1) - 2 and g(x) = 2(2|x + 3|)^2 - 2(2|x + 3|) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4((-1(-1(1|x - 3| + 1)^2 + 2(1|x - 3| + 1) + 1))/(3(-1(1|x - 3| + 1)^2 + 2(1|x - 3| + 1) + 1) + 2)) - 5 and g(x) = -1|(-1(1x - 2)^2 + 2(1x - 2) - 4) - 3| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4(-2|(-2e^(1x) + 2) - 1|) + 5 and g(x) = -3sin(1π(-5x^2 - 1x - 1) - 3) - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3(-3|(-2sin(1π(-4x + 2)) + 2) - 1| + 2)^2 - 3(-3|(-2sin(1π(-4x + 2)) + 2) - 1| + 2) + 1 and g(x) = -3(2((1x + 1)/(1x + 2)))^2 + 1(2((1x + 1)/(1x + 2))) + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|(2sin(3πx + 2) + 1) - 2| - 3 = 1x^2 + 4x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1cos(2π(-1x + 3) + 3) + 2 and g(x) = -1x^2 - 2x + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(3(5x + 5)^2 + 3(5x + 5)) - 3)/(-3(3(5x + 5)^2 + 3(5x + 5)) + 2) and g(x) = -3e^(-1((2x - 2)/(3x + 1))) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3|(1(3x^2 + 2) + 3)| - 3 and g(x) = 3|(5x - 2)| + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3sin(1π(-5(-1|((3x + 1)/(2x - 1)) - 2| + 1)^2 - 4(-1|((3x + 1)/(2x - 1)) - 2| + 1) + 2)) and g(x) = 1|(1cos(2π((1x + 3)/(1x + 2))) - 1) - 1| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3((-1(1|(4x + 3) - 2| + 2) + 3)/(-2(1|(4x + 3) - 2| + 2) - 2))^2 - 3((-1(1|(4x + 3) - 2| + 2) + 3)/(-2(1|(4x + 3) - 2| + 2) - 2)) and g(x) = 3((1(-4x^2) + 3)/(1(-4x^2))) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(4(1(-2|x + 2| + 3)^2 + 4(-2|x + 2| + 3) - 3) - 4) - 2)/(-3(4(1(-2|x + 2| + 3)^2 + 4(-2|x + 2| + 3) - 3) - 4)) = 3sin(1π(-5((2x + 3)/(-2x - 3))^2 + 3((2x + 3)/(-2x - 3)) - 3) - 3) + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-1cos(2πx - 2))^2 - 5(-1cos(2πx - 2)) - 3 and g(x) = 4x^2 - 2x - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(3|(2cos(3πx + 2) + 1) - 3|) - 3)/(3(3|(2cos(3πx + 2) + 1) - 3|) + 3) and g(x) = -1cos(3π(-3x^2 + 2) - 3) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1sin(1π((-1(1x^2 + 1x + 3) - 2)/(1(1x^2 + 1x + 3))) - 1) - 2 and g(x) = 5(4x + 5)^2 + 4(4x + 5) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2|(-1x^2 + 2x - 2)| - 2 and g(x) = 3x^2 + 4x - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3sin(3π(4x + 1)) - 1 and g(x) = 1x - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(-3cos(3πx)))/(3(-3cos(3πx)) + 3) = -3|x - 3| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(-3cos(1πx + 2) - 3)^2 + 2(-3cos(1πx + 2) - 3) and g(x) = (-1x - 1)/(-2x + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(1|(2(2sin(3πx - 3) + 2)^2 - 1(2sin(3πx - 3) + 2) - 1)| + 1) + 2 and g(x) = -5(-1sin(2π(-3|x - 2| + 2) - 2) + 1) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1((-2(-1sin(3π(-1x^2 + 4x - 3) - 2)) - 3)/(3(-1sin(3π(-1x^2 + 4x - 3) - 2)) - 1)) + 2 and g(x) = -1e^(1((-1(3|x - 3| - 3) - 1)/(1(3|x - 3| - 3) + 2))) - 1 intersect in the interval [-10, 10].

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[User]
Determine the number of intersection points between the functions f(x) = -2|(-2sin(3π(-3((1x - 2)/(1x)) - 3) - 2) + 2) - 3| + 2 and g(x) = (-1(4(1cos(2πx + 1) + 3)^2 - 2(1cos(2πx + 1) + 3) + 5))/(3(4(1cos(2πx + 1) + 3)^2 - 2(1cos(2πx + 1) + 3) + 5) + 3) where -10 ≤ x ≤ 10.

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[User]
How many points of intersection exist between the functions f(x) = 3sin(2π(-2|x - 3| + 2) + 1) + 1 and g(x) = 1x^2 + 4x - 3 in the range -10 ≤ x ≤ 10?

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[User]
Determine the number of intersection points between the functions f(x) = -1|(1((-1x)/(-1x + 2))^2 + 3((-1x)/(-1x + 2)) - 2) - 1| + 3 and g(x) = (2(1x^2 + 3x + 4) + 1)/(-2(1x^2 + 3x + 4) - 2) where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = 4((3(2cos(1πx - 1)) + 2)/(2(2cos(1πx - 1)) - 1))^2 + 3((3(2cos(1πx - 1)) + 2)/(2(2cos(1πx - 1)) - 1)) - 4 and g(x) = (-3(3x^2 - 3x - 3) - 1)/(-1(3x^2 - 3x - 3) + 3) where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = -2(-3|x - 1| - 1)^2 - 4(-3|x - 1| - 1) + 3 and g(x) = 2x - 2 where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = 5(4x^2 - 3x - 1) + 5 and g(x) = (-3x)/(-1x + 3) where -10 ≤ x ≤ 10.

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[User]
How many points of intersection exist between the functions f(x) = (1(-1(-2|x + 2| - 3) - 3) + 3)/(3(-1(-2|x + 2| - 3) - 3) + 1) and g(x) = 1cos(1π((3x - 2)/(-2x + 1)) + 1) + 2 in the range -10 ≤ x ≤ 10?

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[User]
Determine the number of intersection points between the functions f(x) = (-1(4(3|x - 3| - 2) - 2) + 1)/(-1(4(3|x - 3| - 2) - 2) - 3) and g(x) = 3cos(3π(-2x)) where -10 ≤ x ≤ 10.

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[User]
How many points of intersection exist between the functions f(x) = -1e^(1(1|x - 2| - 3)) and g(x) = -5x + 5 in the range -10 ≤ x ≤ 10?

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[User]
How many points of intersection exist between the functions f(x) = 4((-1(1e^(-1x) + 1) + 2)/(2(1e^(-1x) + 1) - 3)) + 1 and g(x) = -1sin(2π((-1x - 2)/(-1x - 1)) + 2) in the range -10 ≤ x ≤ 10?

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[User]
How many solutions does the equation 3cos(1π(-1(2|((1x + 1)/(3x - 2))| - 3)^2 - 3) + 2) + 2 = -4((-2(-1sin(3πx - 3) + 1))/(-3(-1sin(3πx - 3) + 1) + 2))^2 - 1((-2(-1sin(3πx - 3) + 1))/(-3(-1sin(3πx - 3) + 1) + 2)) + 5 have for x in the interval [-10, 10]?

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[User]
Determine the number of intersection points between the functions f(x) = -4((3(-5x - 2) + 1)/(1(-5x - 2) + 1))^2 + 2((3(-5x - 2) + 1)/(1(-5x - 2) + 1)) + 1 and g(x) = -2|(-3x + 5) + 1| - 1 where -10 ≤ x ≤ 10.

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[User]
How many solutions does the equation (-2(-3x^2 - 1) - 1)/(-3(-3x^2 - 1) + 1) = 2|x + 2| - 1 have for x in the interval [-10, 10]?

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[User]
How many solutions does the equation 3(-2e^(-1x) + 3)^2 + 5(-2e^(-1x) + 3) - 1 = -2x^2 - 1x + 3 have for x in the interval [-10, 10]?

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[User]
Find the number of times the graphs of f(x) = -1|(1((-1(3x^2 + 1x) - 1)/(2(3x^2 + 1x) + 1)) - 2) - 1| - 1 and g(x) = -3((-2(2|x - 2| - 1) + 1)/(2(2|x - 2| - 1) + 3)) - 3 intersect in the interval [-10, 10].

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[User]
Determine the number of intersection points between the functions f(x) = 3sin(2π(1(-4(1|x + 2|) + 3)^2 - 4(-4(1|x + 2|) + 3) + 3) + 3) and g(x) = (-1(-2|(-2sin(1πx + 1) - 2) + 1|) + 2)/(2(-2|(-2sin(1πx + 1) - 2) + 1|) + 3) where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = 3sin(1π(2x^2 + 1x - 5) + 1) and g(x) = (1x - 3)/(2x + 2) where -10 ≤ x ≤ 10.

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[User]
How many solutions does the equation -2sin(2π((-3(1(2x^2 - 2) - 1) - 2)/(1(1(2x^2 - 2) - 1) - 3)) + 3) + 2 = 1((-1(-2cos(1πx + 1)) - 2)/(1(-2cos(1πx + 1)))) + 1 have for x in the interval [-10, 10]?

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[User]
Determine the number of intersection points between the functions f(x) = -3((2(-2|x - 2| + 3) + 3)/(1(-2|x - 2| + 3) + 3)) - 3 and g(x) = 1(-4x^2 - 2x) + 5 where -10 ≤ x ≤ 10.

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[User]
Find the number of times the graphs of f(x) = -2(-1x + 1)^2 - 4 and g(x) = -2|x + 2| intersect in the interval [-10, 10].

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[User]
Determine the number of intersection points between the functions f(x) = (-1(3|(5x^2 + 2x - 1) - 3| - 2))/(-1(3|(5x^2 + 2x - 1) - 3| - 2) + 2) and g(x) = -2|((2x + 3)/(3x - 1)) - 3| - 3 where -10 ≤ x ≤ 10.

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