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

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


[User]
How many solutions does the equation 3(-3sin(3πx - 1) - 1)^2 - 2(-3sin(3πx - 1) - 1) - 2 = -3|x + 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) = -2|((-1(-1sin(1π(2x^2 + 2x - 3) + 1) - 3) + 1)/(-1(-1sin(1π(2x^2 + 2x - 3) + 1) - 3) - 1))| + 2 and g(x) = 3((-3(2|x - 1| + 1) - 1)/(2(2|x - 1| + 1) + 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) = (-2(3(1(-2|x - 1| + 1) + 4)^2 + 1(1(-2|x - 1| + 1) + 4) + 4) - 1)/(2(3(1(-2|x - 1| + 1) + 4)^2 + 1(1(-2|x - 1| + 1) + 4) + 4) - 1) and g(x) = -3(-5((3x + 2)/(-1x)) + 4)^2 + 4(-5((3x + 2)/(-1x)) + 4) + 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(-5(-2cos(3πx + 3) - 3)^2 + 5(-2cos(3πx + 3) - 3) - 4) + 1 and g(x) = (2(-1|x - 3| + 3) + 3)/(-1(-1|x - 3| + 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) = -1|(-4x + 5) + 2| + 1 and g(x) = (1x)/(2x + 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) = -2((-2(2|(-2cos(2πx + 2) - 3) + 2| - 1) - 2)/(2(2|(-2cos(2πx + 2) - 3) + 2| - 1) + 1)) + 3 and g(x) = 1cos(3π((-3(-3x^2 + 4x + 3) - 2)/(-3(-3x^2 + 4x + 3) + 4)) - 2) + 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) = 4(2sin(2πx - 1) + 1) + 5 and g(x) = 1|x - 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(3sin(3πx - 1) + 3) - 3)/(3(3sin(3πx - 1) + 3) + 1) and g(x) = (2x + 1)/(-3x - 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) = (2(3x^2 + 3x - 5))/(-2(3x^2 + 3x - 5) - 1) and g(x) = 4x^2 + 4x - 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|(-3x + 1) - 1| - 2)^2 - 1(2|(-3x + 1) - 1| - 2) - 1 and g(x) = -2cos(3π((2x - 2)/(-2x + 1)) - 1) - 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(-2(2|x - 2|) - 4)^2 + 2(-2(2|x - 2|) - 4) - 3) + 3)/(3(3(-2(2|x - 2|) - 4)^2 + 2(-2(2|x - 2|) - 4) - 3) + 2) = 1(1((-1x + 1)/(-3x + 1)) + 5)^2 - 2(1((-1x + 1)/(-3x + 1)) + 5) - 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(2e^(1x) - 1) + 2)/(-2(2e^(1x) - 1) - 1) and g(x) = 2x^2 + 5x - 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) = -2(2|((1(1x^2 - 2x + 3))/(-1(1x^2 - 2x + 3) - 3)) + 3| - 3) + 3 and g(x) = -1cos(3π((2(3x^2 - 1x - 5) + 3)/(-3(3x^2 - 1x - 5) + 4)) - 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) = (1(2e^(-2(-4(-1|x + 1| + 3) + 5)) - 3) + 2)/(-2(2e^(-2(-4(-1|x + 1| + 3) + 5)) - 3) - 1) and g(x) = -1|((-2(-4x^2 - 4x + 5) + 3)/(-3(-4x^2 - 4x + 5) + 4)) + 2| + 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(-3cos(1πx - 2) + 3) + 1 and g(x) = 1|x - 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) = 2|(5((-1x + 1)/(2x + 1))^2 - 5((-1x + 1)/(2x + 1)) - 1) - 3| - 1 and g(x) = -3e^(-2(1x^2 - 4x - 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) = 1cos(3π(-2((-3x + 3)/(2x - 1)) + 4) - 1) - 3 and g(x) = 1cos(1π((3x + 1)/(-2x - 1)) - 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) = -2|(4(2x - 4)^2)| + 3 and g(x) = 1(1e^(-1x) - 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) = -2sin(1π(3|x - 3| - 1) + 3) - 2 and g(x) = 2x^2 + 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) = 3((-3x - 3)/(2x - 1))^2 - 4((-3x - 3)/(2x - 1)) + 1 and g(x) = 1x^2 - 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) = -5(-3((-3x + 1)/(3x - 1)) + 3)^2 + 2(-3((-3x + 1)/(3x - 1)) + 3) - 2 and g(x) = (2(2|x + 2| - 3))/(2(2|x + 2| - 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) = -5(-3sin(1π(-1x^2 + 1x + 5) + 3) + 1) + 2 and g(x) = (1(1|x + 3| - 1) - 2)/(3(1|x + 3| - 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(1sin(3π(3|x| + 3) + 2) + 3) + 5 and g(x) = -2|(-2cos(1πx - 2) - 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) = -3sin(2π(-2((-3x - 1)/(2x + 3)) - 2) + 3) - 3 and g(x) = (2(-5x^2 + 4x + 2) - 3)/(1(-5x^2 + 4x + 2) - 2) where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 5(-3sin(1π(5(2|x - 2| + 1) - 5)) + 3)^2 - 2(-3sin(1π(5(2|x - 2| + 1) - 5)) + 3) - 3 = 1sin(3π(1(2|x - 1| - 2) - 4) - 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) = -2sin(2π((-2x + 2)/(-2x + 3)) - 3) - 1 and g(x) = -3|x + 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) = -2|(-5x^2 - 4x + 4) + 2| - 1 and g(x) = 5x + 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(2|(-1((-1x + 3)/(-3x))^2 + 2((-1x + 3)/(-3x)) + 3) - 1| - 2) - 5 and g(x) = -2cos(3π(-2((-2x - 3)/(1x - 3)) + 5)) - 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(2|x - 2| - 1)^2 - 3(2|x - 2| - 1) - 4) - 2)/(-3(3(2|x - 2| - 1)^2 - 3(2|x - 2| - 1) - 4)) and g(x) = 1|(-3x^2 + 1x + 4)| + 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) = 3cos(2π(2x + 1) + 1) - 3 and g(x) = -5x^2 + 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((2x + 2)/(2x - 1))^2 + 5((2x + 2)/(2x - 1)) - 1 and g(x) = 3|x - 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) = -1sin(1π(-1x^2 + 4x + 1) + 1) and g(x) = -2x - 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(-2sin(3π(3x^2 - 4x + 4) - 1) - 1) + 1)/(1(-2sin(3π(3x^2 - 4x + 4) - 1) - 1) + 2) and g(x) = -1sin(3π(2|x + 3| - 1) - 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) = -2cos(2π((-3x + 3)/(-2x)) - 2) - 2 and g(x) = 3|x + 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((-1(-2e^(1x) + 3) - 2)/(2(-2e^(1x) + 3) + 3))^2 - 4((-1(-2e^(1x) + 3) - 2)/(2(-2e^(1x) + 3) + 3)) + 3 and g(x) = (1(-3x - 5) + 1)/(3(-3x - 5) - 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(-1sin(1π((-1x)/(-2x - 1)) + 3))^2 - 2 and g(x) = 2|((2x - 1)/(2x - 1)) - 1| - 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|(1((-3(-3x - 2) - 1)/(-2(-3x - 2) + 3))^2 - 1((-3(-3x - 2) - 1)/(-2(-3x - 2) + 3)) + 2) - 1| - 2 and g(x) = -1(2|(2x^2 - 3x + 1) + 2| + 1) + 5 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -1(-3(1cos(3π(1|x| - 2) + 2) + 2)^2 - 2) = 5((1(2e^(1x)) - 1)/(1(2e^(1x)) + 3))^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) = 1|((-2(1cos(1πx - 1) - 1) - 1)/(2(1cos(1πx - 1) - 1) - 3)) - 1| + 3 and g(x) = 4((1x - 1)/(-3x + 2))^2 - 5((1x - 1)/(-3x + 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(-1e^(-1x) + 1)^2 - 3(-1e^(-1x) + 1) + 5 and g(x) = 4x + 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(1|(1e^(-1x) + 2) + 1| - 2) - 2)/(2(1|(1e^(-1x) + 2) + 1| - 2) + 3) and g(x) = 1(3x^2 + 5x - 4) - 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) = 3(3|((-1(-5x^2 + 4x - 4) + 1)/(1(-5x^2 + 4x - 4) - 2))| - 1) and g(x) = 1|(-1(-1x - 4)^2 + 2(-1x - 4) + 4) - 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) = (2(1(1|x| - 2) - 3) - 3)/(3(1(1|x| - 2) - 3)) and g(x) = (-2(-3|x| - 1) + 1)/(2(-3|x| - 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) = -2(3|((1x - 1)/(-1x - 1)) + 3| - 1) and g(x) = 2sin(2π(5x + 4) + 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|(-2x + 1) - 3| + 3 and g(x) = 5x^2 + 3x 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(1π(1|(3(5x - 1)^2 - 3(5x - 1)) - 2| - 1) + 2) - 3 and g(x) = 2((1(-1|x - 1|) - 1)/(-1(-1|x - 1|) + 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) = -1|((3(-2(1x^2 - 2x + 3) + 5) + 1)/(2(-2(1x^2 - 2x + 3) + 5) + 3)) - 3| - 3 and g(x) = -1|(-2e^(2((3x)/(-2x + 1))) + 1) - 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((-3(-2|x| - 2) - 1)/(-2(-2|x| - 2) + 3)) - 5 and g(x) = -1(4x^2 - 3x - 1) + 4 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -1(2x^2 + 5x + 2) + 1 = (2x + 2)/(-2x - 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(-3cos(1π(1|x - 2| + 3) + 3) - 1) - 2)/(-2(-3cos(1π(1|x - 2| + 3) + 3) - 1) + 1) and g(x) = -3|(2sin(1πx - 2) + 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|(-3sin(2πx - 2) - 3) - 3| + 3 = -3|x - 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 -1|((-3x - 1)/(-1x - 1)) + 1| + 3 = -2|x - 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 2((-2(-3|x - 1| + 1) + 2)/(-2(-3|x - 1| + 1) - 2)) + 4 = 3cos(2π((2x - 1)/(2x)) + 2) - 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((2(-1|(-1x^2 - 4x - 2) - 3| - 3) + 2)/(1(-1|(-1x^2 - 4x - 2) - 3| - 3) - 3)) - 4 and g(x) = -1(-3|(-1cos(2πx + 2) + 2) + 1| + 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(-3cos(2π(-1|x + 3| - 3) - 3) - 2) + 4 = -2cos(3π(1|x| - 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) = 2(3|(-1sin(2π((-3x - 1)/(-1x + 2)) + 3) + 1)|) - 4 and g(x) = -3((-2(-3|x - 3| + 3) - 3)/(2(-3|x - 3| + 3) + 1)) - 4 in the range -10 ≤ x ≤ 10?

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


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

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


[User]
How many solutions does the equation 5(1e^(-1x) - 3) - 5 = -5x^2 - 3x - 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) = 3cos(3π(-1|x + 1| - 1) - 3) - 3 and g(x) = -3|x + 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(-1(-1sin(3π(4x - 1) - 3) + 1)^2 - 4(-1sin(3π(4x - 1) - 3) + 1) + 3) - 2)/(-1(-1(-1sin(3π(4x - 1) - 3) + 1)^2 - 4(-1sin(3π(4x - 1) - 3) + 1) + 3) + 2) and g(x) = 4(5(3|x| - 2)^2 - 3(3|x| - 2) - 4) + 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(2e^(1(-2x - 1)) + 1) - 1)/(3(2e^(1(-2x - 1)) + 1) - 2) and g(x) = -3cos(1π((-2x + 2)/(3x - 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) = (1(-1x^2 - 1x - 4) + 3)/(-1(-1x^2 - 1x - 4)) and g(x) = -4x^2 - 1x + 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) = -1(1sin(1πx - 3))^2 + 5(1sin(1πx - 3)) + 2 and g(x) = -1x^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) = (1(-1sin(3π(-4(-5x^2 + 2x + 5) + 3) + 3) + 2) + 3)/(2(-1sin(3π(-4(-5x^2 + 2x + 5) + 3) + 3) + 2)) and g(x) = 2|(4(-2e^(2x) + 3)^2 + 3(-2e^(2x) + 3) - 4) - 2| - 1 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -2sin(2π(2|(-1(-2x + 5)^2 + 2) - 3| + 2)) + 3 = 3(-5((-3x - 3)/(2x))^2 - 1((-3x - 3)/(2x)) + 1) + 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) = -3sin(3π((-2(2(4x + 4)^2 + 3(4x + 4) + 5))/(-2(2(4x + 4)^2 + 3(4x + 4) + 5) + 3)) - 3) - 2 and g(x) = 3e^(-2((-1(2x - 1) + 2)/(-1(2x - 1) - 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) = -1((1(-2|x - 1| + 3) + 1)/(2(-2|x - 1| + 3) + 1))^2 - 1 and g(x) = -2|(2x - 3) + 1| + 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) = (2(-3(-4x^2 + 2x + 3) + 4) - 3)/(1(-3(-4x^2 + 2x + 3) + 4)) and g(x) = 1|((3x + 3)/(-2x + 3)) - 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) = -1sin(2π(3(5(1|x + 2| - 1)^2 - 4(1|x + 2| - 1) + 5) + 2) + 2) and g(x) = -1|(2(-1x)^2 - 1(-1x)) + 2| + 2 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -3(3e^(-1x) - 2)^2 + 2(3e^(-1x) - 2) + 1 = (3x + 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|(4(3sin(3π((2x + 1)/(-1x + 3)) + 3) + 2) + 2)| + 1 = 5(-5(3cos(2πx - 3) + 1)^2 + 4(3cos(2πx - 3) + 1) + 2) - 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|(3(-2e^(1x) - 1)^2 - 5(-2e^(1x) - 1) - 2) - 3| and g(x) = -5((-2x)/(-3x - 1))^2 - 1((-2x)/(-3x - 1)) + 2 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -2(1(-3|((-2x + 3)/(-1x + 3))| + 1)^2 + 1(-3|((-2x + 3)/(-1x + 3))| + 1) - 3) - 3 = (2(-3e^(1(2|x + 1| + 3)) + 1) + 1)/(1(-3e^(1(2|x + 1| + 3)) + 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) = (-1(-2(4x^2 - 1x - 4) - 5) + 1)/(3(-2(4x^2 - 1x - 4) - 5) + 3) and g(x) = 1(4x^2 + 5x - 5) + 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(3|((2(-3sin(3πx + 2) + 3) - 2)/(1(-3sin(3πx + 2) + 3) + 1)) - 1| - 2) + 2 and g(x) = (3(3(-3|x + 3| - 1)^2 - 3(-3|x + 3| - 1) + 5) - 2)/(-3(3(-3|x + 3| - 1)^2 - 3(-3|x + 3| - 1) + 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) = 2|(-1cos(2π((-1(4x^2 + 1x - 5) - 3)/(3(4x^2 + 1x - 5) - 2)) + 1) - 2) + 2| + 1 and g(x) = -1(-3((3x + 1)/(3x - 2)) + 4)^2 - 3(-3((3x + 1)/(3x - 2)) + 4) + 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) = (-2(-3(-2x + 4)^2 - 3(-2x + 4) + 4) - 3)/(-3(-3(-2x + 4)^2 - 3(-2x + 4) + 4) - 3) and g(x) = 1sin(1π(4x^2 - 2x + 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) = (3(3|x| + 3))/(-1(3|x| + 3) + 2) and g(x) = -3|x + 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(1sin(1πx + 3))^2 - 1(1sin(1πx + 3)) - 5 and g(x) = -2|x - 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) = -3sin(2π(-1|((-1(-3x) - 1)/(-1(-3x) + 2)) + 3|) - 2) + 2 and g(x) = 3sin(1π(5((-3x + 2)/(-1x + 3))^2 + 4((-3x + 2)/(-1x + 3)) + 3) - 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(-1|x - 1| - 1)^2 + 5(-1|x - 1| - 1) + 3 = -1x^2 + 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) = 3((-2(-2|(1x^2 - 5x - 1) + 2| - 1) - 3)/(1(-2|(1x^2 - 5x - 1) + 2| - 1))) + 2 and g(x) = -1cos(3π(3(1x^2 + 4x - 5) + 3) - 2) + 1 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -3((3(3|(1cos(2πx - 1) + 1) - 3| - 3) + 3)/(2(3|(1cos(2πx - 1) + 1) - 3| - 3) + 1)) + 1 = (-3(2|(-2x + 4) - 3| - 3) - 3)/(-1(2|(-2x + 4) - 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) = -2(2cos(3πx - 2) + 3)^2 - 3(2cos(3πx - 2) + 3) - 4 and g(x) = 3x - 2 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation (-1(-5(3|x - 3| + 1)^2 - 2(3|x - 3| + 1) + 4) - 2)/(-2(-5(3|x - 3| + 1)^2 - 2(3|x - 3| + 1) + 4) - 3) = 3(2x^2 - 1x - 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) = 3cos(2π(2(5x - 2)^2 - 1(5x - 2) + 2) + 3) + 2 and g(x) = 1|((-2x - 3)/(-2x + 1)) - 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((3(-3(-1|x - 2| - 1)^2 - 2(-1|x - 2| - 1) + 1) - 1)/(3(-3(-1|x - 2| - 1)^2 - 2(-1|x - 2| - 1) + 1) - 2)) + 4 and g(x) = 1(2((3x - 1)/(-1x + 2))^2 - 5((3x - 1)/(-1x + 2)) - 2) - 5 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (-2(2x - 1) + 3)/(-3(2x - 1) + 1) = 3|x - 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|((2x + 3)/(2x + 2)) - 1| and g(x) = -1|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) = -1(1sin(3πx)) - 2 and g(x) = -3|x| + 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) = (1(1|(3x + 3) + 1| - 1) - 1)/(2(1|(3x + 3) + 1| - 1) + 1) and g(x) = -3|(-1sin(1πx + 3) + 1) + 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) = -3cos(3π(5x^2 - 4x + 4) - 2) + 3 and g(x) = 3|x - 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) = 3|((-2x + 2)/(-2x - 3)) + 2| + 2 and g(x) = 4x^2 - 1 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 5(-3cos(3π((-1(-2x - 2) + 1)/(-3(-2x - 2) - 2)) + 3) + 2)^2 - 3(-3cos(3π((-1(-2x - 2) + 1)/(-3(-2x - 2) - 2)) + 3) + 2) - 5 = -2sin(2π(-1|(1x + 5) + 3| + 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 (-3(-3|(-5(1x^2 + 4x - 5) + 3) + 1| + 2))/(2(-3|(-5(1x^2 + 4x - 5) + 3) + 1| + 2) + 3) = 3((2(2x^2 - 5x) - 1)/(2(2x^2 - 5x) + 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|(3((3(-5x^2 + 2x - 3) - 1)/(-3(-5x^2 + 2x - 3) - 2)) - 1) + 3| + 2 and g(x) = 2((2(1sin(3πx + 2) + 1) - 1)/(-2(1sin(3πx + 2) + 1) + 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) = -3sin(3π(1(1|x + 2| + 1) + 4) - 1) - 1 and g(x) = -3sin(3π(4x)) + 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(-1|((-1(-2x + 1) + 3)/(3(-2x + 1) + 2)) + 1| + 1)^2 + 1(-1|((-1(-2x + 1) + 3)/(3(-2x + 1) + 2)) + 1| + 1) and g(x) = -2sin(3π(-3(3x^2 + 2x + 2) + 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) = (-3(5x^2 + 2x - 4) + 2)/(2(5x^2 + 2x - 4) - 3) and g(x) = 1|x + 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(-1(-2|((3x + 3)/(-2x + 3)) - 3|) + 3)^2 - 2(-1(-2|((3x + 3)/(-2x + 3)) - 3|) + 3) + 4 and g(x) = -2e^(2(5(1x^2 + 1x - 5) - 4)) - 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(-1((2(2|x - 2| - 1))/(-3(2|x - 2| - 1) + 1)) - 1)^2 - 2(-1((2(2|x - 2| - 1))/(-3(2|x - 2| - 1) + 1)) - 1) - 3 and g(x) = -3|(5(3x^2 - 3x + 2)) - 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) = -1(3((2x + 3)/(2x - 1)) - 4)^2 + 3(3((2x + 3)/(2x - 1)) - 4) - 1 and g(x) = 1cos(3π(1x + 2) + 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|((-2(-5(2x^2 + 3x + 3) - 2) - 1)/(2(-5(2x^2 + 3x + 3) - 2) + 3))| + 1 and g(x) = -2(3|((-1x + 2)/(-3x - 1)) - 1| - 1)^2 - 2(3|((-1x + 2)/(-3x - 1)) - 1| - 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(-2x + 4) - 2)/(3(-2x + 4) - 2) and g(x) = (1x - 1)/(-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) = 3(5((1x + 2)/(2x + 3)))^2 - 5(5((1x + 2)/(2x + 3))) - 2 and g(x) = 4(1sin(3πx) + 3)^2 + 3(1sin(3πx) + 3) - 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(1|(3x^2 - 2x + 2) + 2| - 2))/(-2(1|(3x^2 - 2x + 2) + 2| - 2) - 2) and g(x) = -3cos(1π(-4x^2 - 1) + 2) + 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(2(2|(1x^2 + 4)|) + 3) - 1)/(2(2(2|(1x^2 + 4)|) + 3) - 3) and g(x) = 1cos(2π(-3(1|x + 1| + 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 -1(-2|(3((-1x - 2)/(-3x - 3))^2 - 4((-1x - 2)/(-3x - 3)) - 2) - 2| - 2) + 5 = -4(2sin(1π(-3|x + 3|) - 3) - 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) = 2|(-3cos(2πx - 2) + 3) - 2| - 1 and g(x) = (-2x + 3)/(3x - 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(-2|(-3x^2 - 4x + 3) + 2| + 2) - 1 and g(x) = -1((-2x)/(1x - 3)) - 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) = 1(3sin(1πx - 2) + 1) - 2 and g(x) = -2|x - 1| - 1 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -1sin(3π((1x - 1)/(1x + 3)) - 2) = (1x + 3)/(-2x - 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(-2e^(2(2x + 4)) - 2) - 1)/(1(-2e^(2(2x + 4)) - 2) + 1) = (-3(2x^2 + 5x - 3) - 3)/(-2(2x^2 + 5x - 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) = 5(5(2cos(1π(-3|x - 1| - 1) + 1) + 2)^2 + 5(2cos(1π(-3|x - 1| - 1) + 1) + 2) - 1) - 2 and g(x) = (-2(-2|(-4x + 5)| + 1) - 2)/(-2(-2|(-4x + 5)| + 1)) intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation (1(2cos(2πx - 1) + 2) + 2)/(-1(2cos(2πx - 1) + 2) - 3) = -1x^2 + 2x + 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(-1x + 3) + 2)/(-3(-1x + 3) + 2) = -5x - 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(-5(-3x + 4)^2 - 2(-3x + 4) - 3))/(3(-5(-3x + 4)^2 - 2(-3x + 4) - 3) + 3) = -2(3sin(3πx + 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) = (-2(4(1|(2sin(2πx - 2) + 1) + 2| - 1) + 3))/(-3(4(1|(2sin(2πx - 2) + 1) + 2| - 1) + 3) + 4) and g(x) = 3e^(-1(1(-2|x + 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) = 2|((-3(4x - 2))/(3(4x - 2) + 3)) + 3| + 2 and g(x) = 1e^(1(-2|x + 1| + 2)) + 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|((-2x - 3)/(1x - 2)) - 3| + 3 and g(x) = 3x^2 + 2x - 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(3|(-4(-1x^2 - 5x - 4) + 5) - 3|) + 3)/(1(3|(-4(-1x^2 - 5x - 4) + 5) - 3|) - 2) and g(x) = -1|(3e^(1(1x^2 - 2x - 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) = (2(1|(1(-3x - 4)^2 + 3(-3x - 4) - 1) + 3| - 2) - 1)/(-2(1|(1(-3x - 4)^2 + 3(-3x - 4) - 1) + 3| - 2)) and g(x) = (1(2cos(1π(1x + 3) - 3) + 1) + 1)/(-2(2cos(1π(1x + 3) - 3) + 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) = 5(2sin(1πx + 2) - 2) + 3 and g(x) = (-1x - 3)/(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) = 1((2(-1|(-4x^2 - 2x - 1) + 2| - 2) + 3)/(2(-1|(-4x^2 - 2x - 1) + 2| - 2) + 3)) - 1 and g(x) = (-2(-5(3|x - 2| - 1) - 2) + 1)/(-3(-5(3|x - 2| - 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(-1x - 4))/(-1(-1x - 4) - 1) and g(x) = 1x^2 - 5x - 4 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 5(-1((-1(-2|x - 1| - 1) - 3)/(-3(-2|x - 1| - 1) - 3))^2 - 3((-1(-2|x - 1| - 1) - 3)/(-3(-2|x - 1| - 1) - 3)) - 3) + 4 = -1|(3((-2x + 3)/(-2x)) - 1) - 2| - 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) = 3|(3e^(-1(1(1x + 5)^2 - 1(1x + 5))) + 2) - 2| - 1 and g(x) = (2(5(-1x^2 - 2x - 1) + 5) - 1)/(1(5(-1x^2 - 2x - 1) + 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) = (3(2(-3(2|x - 2|)^2 + 4(2|x - 2|) - 1) + 5) - 1)/(-2(2(-3(2|x - 2|)^2 + 4(2|x - 2|) - 1) + 5) + 3) and g(x) = (-3(2e^(1(-2|x + 3| + 3)) + 1) + 1)/(-2(2e^(1(-2|x + 3| + 3)) + 1) - 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) = 2|(-2(-2((3x - 3)/(1x + 1)) + 2)^2 + 2(-2((3x - 3)/(1x + 1)) + 2) + 1) - 3| + 2 and g(x) = -1(1e^(-1(-1|x - 1| + 2)) - 2)^2 - 3(1e^(-1(-1|x - 1| + 2)) - 2) + 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|(-3((-3x + 1)/(3x + 2)) + 4) - 2| - 1)^2 - 3(3|(-3((-3x + 1)/(3x + 2)) + 4) - 2| - 1) - 2 and g(x) = (-3(-1(-2sin(2πx + 1) + 3) + 2) + 3)/(2(-1(-2sin(2πx + 1) + 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(1(-2|((-1x - 1)/(-1x + 2)) - 2| + 3) - 5)^2 + 5(1(-2|((-1x - 1)/(-1x + 2)) - 2| + 3) - 5) - 4 = 1|((1(2x - 3) + 2)/(1(2x - 3) - 2)) - 2| + 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|(-4(-2e^(-1x) + 3)^2 + 4)| = 1|(-1x^2 - 5x - 4) + 1| + 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) = -3((3(4x + 5) + 3)/(3(4x + 5) - 2))^2 + 2((3(4x + 5) + 3)/(3(4x + 5) - 2)) and g(x) = 1cos(1π(5x^2 + 2x - 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) = (1(2(-3cos(3π(-1|x + 2| + 1) + 1) - 2) + 3) - 2)/(-3(2(-3cos(3π(-1|x + 2| + 1) + 1) - 2) + 3) - 3) and g(x) = 1cos(1π(-5(4x^2 + 2x - 5) - 1) - 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|(-1sin(2π(1x + 2) - 2)) + 3| + 1 = 1(2e^(2x)) - 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 -4(5(-2cos(1πx + 1) + 1) + 2)^2 - 2(5(-2cos(1πx + 1) + 1) + 2) + 2 = -3(-3|x - 1| + 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) = 2(2|(-2sin(1π((2x - 1)/(3x))) - 2) - 3| - 3) + 4 and g(x) = 3|(-1cos(1π(4x - 1)) + 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|((-1(3e^(2x) + 3))/(-2(3e^(2x) + 3) + 3)) - 3| + 2 = 1|(3sin(2πx) - 1) + 1| - 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(-2cos(3π(-4(5x^2 - 4x)) - 3) + 2) + 2)/(-1(-2cos(3π(-4(5x^2 - 4x)) - 3) + 2) + 2) and g(x) = 1(2sin(2π(-1|x - 2| + 1) - 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) = -5(4((3x + 2)/(-1x - 1))^2 - 1((3x + 2)/(-1x - 1)) - 1) and g(x) = -3(1sin(1πx - 1) + 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(-1((2(3|x + 3| - 2) + 3)/(1(3|x + 3| - 2) + 3))^2 + 4((2(3|x + 3| - 2) + 3)/(1(3|x + 3| - 2) + 3)) - 2) - 3 = -2|(3(-2e^(2x) + 1) + 4) - 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) = -1|((-2(4(-5x + 3)^2 - 1(-5x + 3) - 4) + 3)/(3(4(-5x + 3)^2 - 1(-5x + 3) - 4) + 2)) + 1| and g(x) = 1|((-1(4x^2 - 2) + 1)/(2(4x^2 - 2) - 1)) + 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) = 1(-1(1|((-3x - 3)/(2x - 3)) - 2| - 1) + 3)^2 - 4(-1(1|((-3x - 3)/(2x - 3)) - 2| - 1) + 3) - 4 and g(x) = -3cos(2π(-2((-2x - 3)/(-2x - 1)) - 1) - 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) = -4(-2cos(1πx - 3) + 2)^2 - 3(-2cos(1πx - 3) + 2) + 5 and g(x) = 1x^2 - 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) = -2sin(1π(1((1(2x^2 - 4) + 2)/(-2(2x^2 - 4) + 3)) - 4)) + 2 and g(x) = (-3(1(1x^2 + 2x - 4) + 4) + 1)/(-2(1(1x^2 + 2x - 4) + 4) + 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) = -5(3sin(1πx) - 1)^2 - 2(3sin(1πx) - 1) + 5 and g(x) = 1|x + 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) = -3|((-2(-4x^2 - 5x - 4) - 2)/(-1(-4x^2 - 5x - 4)))| - 3 and g(x) = -1(-3sin(2πx + 1) + 2)^2 - 3(-3sin(2πx + 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) = -1e^(2((-1(5x^2 - 5x - 4) - 2)/(-3(5x^2 - 5x - 4) - 2))) + 2 and g(x) = (2(1sin(3πx) + 2) - 3)/(2(1sin(3πx) + 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(-2e^(1(-2|x| + 3)) + 1)) - 1)/(2(2(-2e^(1(-2|x| + 3)) + 1)) + 3) and g(x) = -4((3(3x^2 - 1x - 4) + 2)/(-1(3x^2 - 1x - 4) - 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(-2|(-4((1x - 1)/(2x)) - 4) + 3| + 2)^2 + 1(-2|(-4((1x - 1)/(2x)) - 4) + 3| + 2) - 4 and g(x) = (1(-1sin(3π(2|x + 1| + 3) + 2) - 2))/(-2(-1sin(3π(2|x + 1| + 3) + 2) - 2) + 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(-2(-1|((-1x + 1)/(-2x + 1)) + 1| - 1) + 3)^2 - 1 and g(x) = 2(5((3x + 3)/(-2x + 3))^2 - 1((3x + 3)/(-2x + 3)) - 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|(1(1sin(3π(2x + 4) - 3))^2 - 3(1sin(3π(2x + 4) - 3)) - 1) + 2| - 2 and g(x) = (-1(1sin(2π(-1x + 4) + 2) - 2) - 2)/(3(1sin(2π(-1x + 4) + 2) - 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) = 4((-1(-1|(2e^(-1x)) + 1| + 1) + 3)/(2(-1|(2e^(-1x)) + 1| + 1) + 1)) + 4 and g(x) = 1cos(3π(5(-3|x - 2| + 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) = 3sin(1π(3(-2x - 2)^2 + 5(-2x - 2) + 2) + 3) + 3 and g(x) = 3(2sin(3πx - 3) + 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) = (-2(-1|(5x)| + 1) + 3)/(2(-1|(5x)| + 1) + 2) and g(x) = -4(3|x|) + 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) = 1cos(3π((-2(3(-5x + 2)^2 - 3) - 2)/(-2(3(-5x + 2)^2 - 3))) + 3) - 1 and g(x) = 3cos(3π(-5((3x + 3)/(3x)) + 2) + 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 + 3) - 1)/(2(1x + 3) - 1) = 3x + 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 -5((-2(1|(-2x + 5) - 2| - 3) + 3)/(-2(1|(-2x + 5) - 2| - 3) - 1))^2 + 5((-2(1|(-2x + 5) - 2| - 3) + 3)/(-2(1|(-2x + 5) - 2| - 3) - 1)) + 3 = (3(3(4x - 2)^2 - 2(4x - 2) - 1) + 3)/(-1(3(4x - 2)^2 - 2(4x - 2) - 1) - 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|(-3cos(3πx + 2) - 2) + 1| + 1 and g(x) = 4x + 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) = 2|(1(-3x^2 - 1x + 4) - 4) + 1| - 3 and g(x) = 3sin(2π(2|x + 2| - 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) = -3(-4(3|((-2x - 3)/(3x + 3)) - 1| - 2)^2 - 1(3|((-2x - 3)/(3x + 3)) - 1| - 2) + 1) - 4 and g(x) = 2sin(1π(-1(1|x - 3| + 3)^2 - 5(1|x - 3| + 3) - 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|(3cos(3π(1((1x - 1)/(-3x + 1))^2 + 1((1x - 1)/(-3x + 1)) - 2) + 3) + 2) - 2| + 3 and g(x) = -3(-2cos(3π(2|x| - 1) + 2) + 1) + 5 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (-2(3|(4(-1x + 3)^2 + 2(-1x + 3) - 4) - 2| - 3) + 1)/(-1(3|(4(-1x + 3)^2 + 2(-1x + 3) - 4) - 2| - 3)) = 1sin(1π(-2|(-4x^2 + 2x + 4)| - 1) - 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) = 1((-2(5x) + 3)/(2(5x) + 2))^2 - 1((-2(5x) + 3)/(2(5x) + 2)) - 5 and g(x) = (-2(-3x^2 + 4x - 4))/(-1(-3x^2 + 4x - 4) - 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(-2x + 1) + 2) and g(x) = 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) = -4(-2x^2 - 5x - 1) + 2 and g(x) = (2x + 3)/(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) = (2(-3|x + 2| + 1) + 2)/(1(-3|x + 2| + 1) - 3) and g(x) = -2|x - 2| + 2 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -4(2|((-1x)/(2x - 3)) + 1| - 3) + 1 = 1(5x + 3)^2 + 5(5x + 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) = (2(-4x^2 - 2x + 4) - 1)/(3(-4x^2 - 2x + 4) + 3) and g(x) = 1|x - 1| + 1 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 2|(-5(-3sin(3πx))^2 - 3(-3sin(3πx)) + 3) + 3| + 3 = (1(-2x^2 + 4x - 1) - 2)/(1(-2x^2 + 4x - 1) + 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) = 1|(-4(2sin(2π(5x - 4) - 3))^2 + 3(2sin(2π(5x - 4) - 3)) + 3) - 3| - 2 and g(x) = (2(-1sin(3π(-2|x - 3| - 3) - 2) + 2) + 3)/(3(-1sin(3π(-2|x - 3| - 3) - 2) + 2) + 2) where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 2|((-2x)/(-3x - 1)) + 2| - 2 = 1x^2 + 2x + 4 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|(1x - 1) + 1| + 2) - 1)/(2(-1|(1x - 1) + 1| + 2)) and g(x) = (2(-1cos(3πx + 1) + 2) + 3)/(-2(-1cos(3πx + 1) + 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) = -1|((2(-1(-4x^2 - 5x) + 3) - 2)/(-1(-1(-4x^2 - 5x) + 3) + 2)) + 2| - 2 and g(x) = -1(-2cos(1π(-3|x - 2| - 3) + 1) - 3)^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) = (-1(1(-2|x| + 1)^2 - 5(-2|x| + 1) - 2) + 3)/(2(1(-2|x| + 1)^2 - 5(-2|x| + 1) - 2) - 1) and g(x) = 2(-4x - 4)^2 - 5(-4x - 4) - 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) = 5((3(-2|(2x - 2) + 2| + 3))/(-1(-2|(2x - 2) + 2| + 3) - 1))^2 + 3((3(-2|(2x - 2) + 2| + 3))/(-1(-2|(2x - 2) + 2| + 3) - 1)) + 4 and g(x) = -5(-3|(-3x^2 - 3x - 5)| + 1) - 1 intersect in the interval [-10, 10].

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


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

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


[User]
How many solutions does the equation (-2(-1(3|(-1x - 1) - 2| + 2)^2 + 4(3|(-1x - 1) - 2| + 2) + 4) - 1)/(2(-1(3|(-1x - 1) - 2| + 2)^2 + 4(3|(-1x - 1) - 2| + 2) + 4) + 3) = -3((1(-1|x|) - 2)/(-2(-1|x|) + 1))^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|(-2sin(1πx + 2) - 3) + 3| + 2 and g(x) = 1x^2 - 5x + 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|(5(-3cos(2πx + 3) - 3) + 5) + 2| + 2) - 3)/(-1(-1|(5(-3cos(2πx + 3) - 3) + 5) + 2| + 2) + 2) and g(x) = -2|(2cos(3π(-2x^2 - 2x + 5) + 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) = 2|(-1(-1e^(-2((-3x)/(-1x))) + 3) - 3) + 1| - 1 and g(x) = 1e^(-2(-1((-3x - 2)/(-3x - 1))^2 + 5((-3x - 2)/(-3x - 1)) - 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(-1|(1e^(-1x) - 2) - 2| + 1) and g(x) = -1sin(3π((2x + 3)/(-3x + 4)) - 1) + 3 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (3(3x + 4))/(2(3x + 4) + 3) = 1|x - 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) = -1sin(3π(-1x - 4) - 1) and g(x) = -2x - 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(1cos(3π(-2|((-2x - 1)/(2x + 2)) - 2| - 3) - 1) + 2)^2 + 5 and g(x) = (-3(-3e^(-2(3x)) + 1) + 2)/(3(-3e^(-2(3x)) + 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) = -3sin(3π(2((-2x - 2)/(1x - 3))^2 - 4((-2x - 2)/(1x - 3)) - 5) + 3) - 2 and g(x) = (-1(1e^(2x) + 1) + 1)/(2(1e^(2x) + 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) = -3(-1|x + 3| + 1)^2 - 3(-1|x + 3| + 1) + 5 and g(x) = -5x 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(-4(3sin(2πx - 3) + 2)^2 - 2(3sin(2πx - 3) + 2) + 5) - 1) + 2)/(2(2(-4(3sin(2πx - 3) + 2)^2 - 2(3sin(2πx - 3) + 2) + 5) - 1) - 1) and g(x) = 5(-1(-1|x - 1| + 1)^2 + 3(-1|x - 1| + 1) + 3) + 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) = (2(1|(-1(-1x^2 + 4x + 2) + 2) + 1| - 1))/(-3(1|(-1(-1x^2 + 4x + 2) + 2) + 1| - 1) - 3) and g(x) = 3(-1cos(1π((-3x + 1)/(2x - 1)) - 3) + 3)^2 - 2(-1cos(1π((-3x + 1)/(2x - 1)) - 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) = -5((-1(2(2sin(3πx - 1) - 1) - 3) - 3)/(1(2(2sin(3πx - 1) - 1) - 3) - 3))^2 + 3((-1(2(2sin(3πx - 1) - 1) - 3) - 3)/(1(2(2sin(3πx - 1) - 1) - 3) - 3)) and g(x) = 2(-5(1|x - 1| - 1)^2 - 5(1|x - 1| - 1) - 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) = -4(-1sin(1πx) + 1)^2 - 3 and g(x) = -2|x - 3| intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation 4(-1sin(1πx + 3) + 2)^2 - 5(-1sin(1πx + 3) + 2) + 1 = 2|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) = 4(-2|((-1x + 1)/(-2x - 2)) + 2| + 2) - 3 and g(x) = 2cos(1π(-2x^2 + 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) = (-2(-2(5(1|x + 3| - 3)^2 - 5) + 5) - 2)/(2(-2(5(1|x + 3| - 3)^2 - 5) + 5)) and g(x) = 1(-2e^(-1(-1x - 1)) - 3)^2 + 4(-2e^(-1(-1x - 1)) - 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((1(3sin(2π(2|x - 2| - 2) - 3) + 1) - 3)/(2(3sin(2π(2|x - 2| - 2) - 3) + 1) - 1)) - 2 and g(x) = 1(-1|(-1e^(1x) + 3) + 1| + 2) - 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(-2cos(1π(2|x - 3| - 2) + 3) + 2)^2 - 5(-2cos(1π(2|x - 3| - 2) + 3) + 2) - 1 and g(x) = -1e^(1(2|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) = (3(1(-1(-1|x| - 1)^2 - 3(-1|x| - 1) - 4) + 3) + 3)/(3(1(-1(-1|x| - 1)^2 - 3(-1|x| - 1) - 4) + 3) - 2) and g(x) = 5(3|(3e^(2x) - 3) - 3| - 1)^2 - 1(3|(3e^(2x) - 3) - 3| - 1) - 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) = 3(3((-3x + 2)/(-1x - 2))^2 + 1((-3x + 2)/(-1x - 2)) - 5) + 1 and g(x) = -2(1|x - 1| + 2) - 5 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (-1(-1(1|(-1cos(3πx + 1) - 3) + 3| + 2)^2 + 4(1|(-1cos(3πx + 1) - 3) + 3| + 2) - 3) + 2)/(-2(-1(1|(-1cos(3πx + 1) - 3) + 3| + 2)^2 + 4(1|(-1cos(3πx + 1) - 3) + 3| + 2) - 3) + 1) = -2(-4((3x - 2)/(-1x - 1))^2 + 2((3x - 2)/(-1x - 1)) - 4) + 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 2sin(2π(3x + 2) + 1) - 1 = 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 -1cos(2π(2|(-1(1x^2 + 5x - 2) + 4) + 3| - 2) + 1) - 3 = (-3(5(3e^(1x) + 1)^2 - 3(3e^(1x) + 1) - 1) - 1)/(1(5(3e^(1x) + 1)^2 - 3(3e^(1x) + 1) - 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) = 5(2|x - 2|) - 3 and g(x) = 1x 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((-2(-3|x - 2| + 2) - 3)/(-1(-3|x - 2| + 2) - 2)) + 4 and g(x) = -1(-3x^2 - 2x - 3) - 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) = 4((-3x + 3)/(-3x + 1)) and g(x) = 3|x - 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) = 2e^(2((-1x)/(-1x))) and g(x) = 3|x - 2| + 2 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -3cos(1π(-1(2|((-2x - 3)/(-1x - 3)) + 3| - 3)^2 - 4) - 2) + 2 = (1(4(2|x + 3| + 1) + 4) - 2)/(1(4(2|x + 3| + 1) + 4) + 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 -2(1((-2x - 2)/(-3x))^2 - 4((-2x - 2)/(-3x)) - 5) - 4 = 4(-1cos(3πx - 3) + 1) - 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|(-2(-1((-2x + 1)/(-2x - 1)))^2 - 2(-1((-2x + 1)/(-2x - 1))) + 2) - 3| - 1 and g(x) = -3(2(-1|x - 2| - 3)^2 - 4(-1|x - 2| - 3) + 1) + 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) = -3e^(-1(-5(-4((3x + 2)/(1x + 1)) - 2)^2 + 3)) - 2 and g(x) = -2((2(1|x + 2| - 2) + 3)/(3(1|x + 2| - 2) - 2))^2 - 4((2(1|x + 2| - 2) + 3)/(3(1|x + 2| - 2) - 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) = (-3(-1cos(1π(-1|x + 1| - 1) + 2) + 2) + 1)/(-1(-1cos(1π(-1|x + 1| - 1) + 2) + 2) + 2) and g(x) = -3e^(-1((3x - 2)/(-1x - 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) = (-1(-1sin(1π(1|(5x^2 - 1x + 5) - 1| + 3) - 1) - 1) - 1)/(-3(-1sin(1π(1|(5x^2 - 1x + 5) - 1| + 3) - 1) - 1) + 2) and g(x) = -2cos(1π(-1|((-2x - 3)/(-1x - 3)) + 1| - 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) = 1|(1x + 1) - 1| - 2 and g(x) = (-2x + 2)/(-3x + 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) = -3(-3cos(1π(4x^2 + 4x + 4) - 3) + 2) + 4 and g(x) = 3((3x - 2)/(-2x))^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) = 1|(-3(-4((-1x + 1)/(2x + 2))^2 - 1((-1x + 1)/(2x + 2))) - 4) - 3| - 2 and g(x) = (-1(-1sin(3π(-3x^2 - 1x - 1) + 1)))/(1(-1sin(3π(-3x^2 - 1x - 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) = 2|(3x + 5) + 3| - 2 and g(x) = 2x + 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(3cos(3πx - 3) - 1) + 1)/(-3(3cos(3πx - 3) - 1) + 2) and g(x) = 2|x - 2| - 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|(-1x^2 - 5x - 2) - 1| - 3 and g(x) = 2x in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -2|((-1x + 1)/(-2x + 3)) - 2| + 2 = -3x^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(3|(2(4x)^2 + 5(4x) - 3) + 3| - 1) + 1)/(3(3|(2(4x)^2 + 5(4x) - 3) + 3| - 1)) = (1(-3|(1cos(1πx + 3) + 1) - 1| - 3) - 1)/(3(-3|(1cos(1πx + 3) + 1) - 1| - 3) + 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 -5(-1cos(1πx + 1) + 1)^2 - 5(-1cos(1πx + 1) + 1) + 3 = 2|x + 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(-3|(-2x) + 3| + 1) - 1)/(-1(-3|(-2x) + 3| + 1) + 2) and g(x) = 1sin(1π(1|x + 1| + 3) - 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) = -1((3(-1e^(-1x) + 2) + 3)/(-1(-1e^(-1x) + 2) - 2)) - 2 and g(x) = 3cos(3π(2x + 5) - 3) + 3 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation (3(-1x - 4) - 3)/(2(-1x - 4) + 2) = 3x + 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) = 2e^(2(-1|x + 1|)) and g(x) = 1|x - 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) = (-1(-3|(-2e^(-2x) - 1) + 1| + 1) - 2)/(-2(-3|(-2e^(-2x) - 1) + 1| + 1) + 3) and g(x) = -2|(5x) - 3| + 3 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (3(1|(-3cos(3π(1x + 4)) + 3) + 2| - 1) - 3)/(3(1|(-3cos(3π(1x + 4)) + 3) + 2| - 1) - 1) = 1|((-2(2x + 3) - 3)/(1(2x + 3) + 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) = (2(-2|(-1(4x - 3)^2 - 4(4x - 3) + 4) - 2| + 1) - 1)/(1(-2|(-1(4x - 3)^2 - 4(4x - 3) + 4) - 2| + 1) - 2) and g(x) = (1(-2(-1e^(2x) - 2)^2 - 4(-1e^(2x) - 2) + 3) + 2)/(-3(-2(-1e^(2x) - 2)^2 - 4(-1e^(2x) - 2) + 3) - 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(-3e^(-2x) + 2) + 3)/(-1(-3e^(-2x) + 2)))^2 + 4((2(-3e^(-2x) + 2) + 3)/(-1(-3e^(-2x) + 2))) and g(x) = 3cos(3π(2|x + 1| + 2) + 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) = -2((-3(-1|(-4x^2 - 1) + 2| + 1) + 1)/(-1(-1|(-4x^2 - 1) + 2| + 1) - 3)) - 4 and g(x) = -2|(2((-3x + 1)/(2x + 1)) - 2) + 2| - 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) = 3|(-4(3sin(2πx - 3) - 2) - 5) - 3| - 2 and g(x) = -4(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) = 1cos(3π(-3|x - 2| - 2) - 2) and g(x) = (-2x)/(1x - 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((-2(1|x - 1| + 3) - 1)/(1(1|x - 1| + 3) - 3))^2 - 4((-2(1|x - 1| + 3) - 1)/(1(1|x - 1| + 3) - 3))) - 3 = -3|(3(1x^2 + 4x + 4) + 4) + 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) = (-1(3cos(2π(-4(-4x^2 - 3x - 1) + 5)) + 1) - 1)/(-3(3cos(2π(-4(-4x^2 - 3x - 1) + 5)) + 1) - 2) and g(x) = (-1(4(-4x - 5)^2 + 5(-4x - 5) + 3) - 3)/(-3(4(-4x - 5)^2 + 5(-4x - 5) + 3)) in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -1(-3cos(1πx)) + 1 = 1x + 5 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(3πx - 1) + 1) + 1 and g(x) = (2x + 2)/(-2x) intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -1cos(1π(-2|((-1x - 2)/(2x + 2)) + 2| + 1) + 2) = 3|((3x + 1)/(-1x + 3)) - 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) = -2(-2cos(3π((-3x - 1)/(2x + 3)) - 2)) - 5 and g(x) = (2(2cos(3πx - 3)) + 3)/(-2(2cos(3πx - 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((-1(3|(-1cos(3πx - 3) + 3) - 2| - 1))/(2(3|(-1cos(3πx - 3) + 3) - 2| - 1))) - 2 and g(x) = (3(-1(-1sin(1πx + 3) + 1)^2 + 3(-1sin(1πx + 3) + 1) - 2) - 3)/(3(-1(-1sin(1πx + 3) + 1)^2 + 3(-1sin(1πx + 3) + 1) - 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) = -3((3(3|x| - 1) + 2)/(1(3|x| - 1) - 2))^2 + 4((3(3|x| - 1) + 2)/(1(3|x| - 1) - 2)) + 3 and g(x) = 1|(-3sin(2πx - 3)) + 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(-5(-2|x - 3| + 3) - 2) - 1)/(3(-5(-2|x - 3| + 3) - 2) + 2))^2 + 3((3(-5(-2|x - 3| + 3) - 2) - 1)/(3(-5(-2|x - 3| + 3) - 2) + 2)) - 2 and g(x) = 3cos(3π(3|(-5x - 1) + 3|) + 1) - 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|((-1(-1x + 1) + 3)/(-2(-1x + 1) + 1)) + 2| - 1 and g(x) = 4(1sin(1πx - 1) + 1)^2 + 3(1sin(1πx - 1) + 1) - 5 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (-3(4(2(2|x + 2| + 3)^2 + 4(2|x + 2| + 3)) - 4) + 3)/(-2(4(2(2|x + 2| + 3)^2 + 4(2|x + 2| + 3)) - 4) + 3) = 3(1|(-1x + 5) + 2|)^2 - 1(1|(-1x + 5) + 2|) - 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 (-1(2cos(3π(-3|x|) + 1) + 3) - 3)/(-2(2cos(3π(-3|x|) + 1) + 3) + 3) = 1(-2|x - 2| - 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(1cos(1πx - 1) + 1) + 3)/(-3(1cos(1πx - 1) + 1) + 2) = -5x^2 + 5x - 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 1(1e^(-2(2x^2 - 5x - 2)) - 1) = 3(-3|x + 2| - 1)^2 + 4(-3|x + 2| - 1) + 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((2(2x + 2) + 1)/(2(2x + 2) - 3))^2 - 3((2(2x + 2) + 1)/(2(2x + 2) - 3)) - 4 = 1sin(3π(4x - 4) + 3) + 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(-1(-2x + 1)^2 + 5(-2x + 1) + 5) - 3)/(-1(-1(-2x + 1)^2 + 5(-2x + 1) + 5) - 1))| - 1 and g(x) = -2cos(1π(-5((-3x - 3)/(2x - 1))^2 + 4((-3x - 3)/(2x - 1)) + 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 -3(4(-2|x + 2| + 3) - 2)^2 + 1(4(-2|x + 2| + 3) - 2) + 4 = (-3(1cos(3πx + 1) + 2) + 1)/(2(1cos(3πx + 1) + 2) - 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|((3(-4x) - 1)/(3(-4x) - 2)) + 2| - 1 = -5(1e^(1x) - 3)^2 + 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 (-3(2(-4x^2 - 2x + 4) - 2) + 1)/(-2(2(-4x^2 - 2x + 4) - 2) + 3) = 2cos(1π(-5x^2 - 5x - 5) - 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) = -1|(-3(2((1x + 3)/(-2x)) - 4)^2 - 3(2((1x + 3)/(-2x)) - 4) + 2) + 1| + 2 and g(x) = -5((1(-3sin(3πx - 2) - 3) - 3)/(-2(-3sin(3πx - 2) - 3) + 3))^2 + 2((1(-3sin(3πx - 2) - 3) - 3)/(-2(-3sin(3πx - 2) - 3) + 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) = -1sin(1π(-3x^2 - 3x + 3) + 1) + 1 and g(x) = -4x^2 + 4x + 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) = 2sin(1π(-1x^2 - 2x - 4) + 3) - 3 and g(x) = -4x^2 + 4x - 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|(2e^(1(2x^2 - 1x - 5))) + 2| - 3 and g(x) = -2|(4x^2 - 1x - 1) - 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) = (-2(3|(1x + 4) + 1| - 3) + 3)/(1(3|(1x + 4) + 1| - 3) + 2) and g(x) = (3(1x + 2))/(1(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(1(3|((2x)/(3x - 2)) - 3| - 2)^2 + 4(3|((2x)/(3x - 2)) - 3| - 2) + 2) + 4 and g(x) = (-2(-3(3|x - 1| - 1) - 3) + 2)/(-1(-3(3|x - 1| - 1) - 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) = 1((2(-1x^2 - 4x - 1) - 2)/(1(-1x^2 - 4x - 1) + 2)) - 3 and g(x) = (2(3|x - 3| - 3) - 2)/(1(3|x - 3| - 3)) where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 3sin(2π(3|x - 2| - 2) + 1) = -2|x| - 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) = -1cos(3π(-2|(-3x + 5) - 2| - 2) + 2) + 1 and g(x) = 2cos(3π(3x^2 - 4x) - 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(1|(3(2x + 4)^2 - 5(2x + 4) + 3) - 1|) - 2)/(-2(1|(3(2x + 4)^2 - 5(2x + 4) + 3) - 1|) + 3) and g(x) = (3(-2|(-3x) - 3| - 3))/(-1(-2|(-3x) - 3| - 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(2e^(1(-1(5x + 1)^2 + 2(5x + 1) + 2)) - 2) + 1)/(3(2e^(1(-1(5x + 1)^2 + 2(5x + 1) + 2)) - 2) - 2) and g(x) = (-2(-3(-3e^(-1x) - 2) - 1) + 3)/(-3(-3(-3e^(-1x) - 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|(1sin(2π(3x - 2) - 3) - 1) + 3| - 2 and g(x) = (-1(1x^2 - 3x) + 3)/(-1(1x^2 - 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(-5(3cos(2π(4x + 3)) - 1)^2 + 3(3cos(2π(4x + 3)) - 1) + 3) + 1)/(-1(-5(3cos(2π(4x + 3)) - 1)^2 + 3(3cos(2π(4x + 3)) - 1) + 3) - 1) and g(x) = 3cos(3π((2(4x^2 - 4x - 5) - 1)/(3(4x^2 - 4x - 5) - 2)) + 2) + 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|(5(-4x + 1)^2 + 4(-4x + 1) - 4)| - 3) + 3)/(-2(1|(5(-4x + 1)^2 + 4(-4x + 1) - 4)| - 3) - 2) and g(x) = -2cos(1π((3(3x^2 - 1x - 1))/(-1(3x^2 - 1x - 1))) - 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) = (-2(1cos(2πx + 2) - 1) - 3)/(-1(1cos(2πx + 2) - 1) + 3) and g(x) = -1x - 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) = -3cos(2π((1(-2|(-1x + 3) - 2| + 2))/(2(-2|(-1x + 3) - 2| + 2) + 1)) + 1) and g(x) = -1|(1cos(2π((2x - 1)/(-2x - 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(-1|x - 1| + 2) + 1)/(3(-1|x - 1| + 2) - 1) = -3x + 5 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(1sin(1π(-2|x| - 1) + 2) - 1) - 4 and g(x) = (2(3|x - 2| - 2) - 2)/(-1(3|x - 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|((-1x + 1)/(-3x + 1)) - 2| + 1 and g(x) = 4x + 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(2((2x + 3)/(1x - 2))^2 + 1((2x + 3)/(1x - 2)) - 5) - 1 and g(x) = (-2(-3|x - 3| + 1) + 3)/(1(-3|x - 3| + 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(-2|((3x)/(-1x)) - 1| + 1)^2 + 5(-2|((3x)/(-1x)) - 1| + 1) - 1 and g(x) = (2(-2sin(1πx) + 2) - 1)/(3(-2sin(1πx) + 2) - 2) where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -4(-3cos(1π(4(-3|x - 2|) - 2) - 2) - 1)^2 + 2(-3cos(1π(4(-3|x - 2|) - 2) - 2) - 1) + 5 = -2((2(-3x - 5) + 2)/(2(-3x - 5) + 1))^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(3|(2x^2 - 3x - 1) + 1| - 3) + 4) + 2)/(-3(-2(3|(2x^2 - 3x - 1) + 1| - 3) + 4) + 4) and g(x) = (-1(-1(3e^(1x) - 3)^2 - 5(3e^(1x) - 3) + 1) - 1)/(2(-1(3e^(1x) - 3)^2 - 5(3e^(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) = -2sin(1π(-3x^2 - 2x + 2)) and g(x) = (2x - 1)/(-3x + 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) = -2cos(3π(1|(1x + 4) + 2|) + 2) and g(x) = -2(1|x - 1| - 1) - 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(2|x + 1|) - 4 and g(x) = -3x + 2 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -2(1cos(1πx - 3) + 1) + 2 = -3x^2 - 3x + 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((1x + 3)/(-2x - 1))^2 + 2((1x + 3)/(-2x - 1)) - 2 = -1x^2 + 5x - 4 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(-1(4x + 2)^2 - 3(4x + 2) + 5) + 2)/(2(-1(4x + 2)^2 - 3(4x + 2) + 5) + 1) and g(x) = 1(3cos(2πx - 3) + 3)^2 + 3(3cos(2πx - 3) + 3) + 1 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation 1|(-3((2x - 1)/(-1x + 3)))| = 5(-1cos(3πx)) + 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) = 4(1x^2 + 5x + 3) and g(x) = -5x^2 - 2x in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 1((3x - 2)/(2x - 3)) - 5 = 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) = 2e^(-2(2|(-2(-2x^2 + 5x + 5) + 1)| + 2)) - 1 and g(x) = -1(-1|(1sin(2πx - 2) + 2)|) - 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(4(-2|(-2x^2 + 2x + 5) - 1| + 3) + 5) + 2)/(2(4(-2|(-2x^2 + 2x + 5) - 1| + 3) + 5) + 2) and g(x) = (1(3|(-2x - 5)| - 1) - 1)/(-2(3|(-2x - 5)| - 1) + 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) = 5(-5(2e^(1x) - 2) + 2)^2 - 3(-5(2e^(1x) - 2) + 2) + 2 and g(x) = 3|((3x - 1)/(-3x - 1)) - 2| where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 1|((-1(3(5x^2 + 1x - 1) + 1) - 2)/(2(3(5x^2 + 1x - 1) + 1) - 3)) - 3| - 3 = (3(-5(2|x - 2| - 1) - 4) - 3)/(2(-5(2|x - 2| - 1) - 4) - 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) = 3|(-2(3((1x)/(3x)) + 2)^2 + 4(3((1x)/(3x)) + 2) - 4)| - 2 and g(x) = 1|(3(2x)^2 - 3(2x) - 4) + 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) = 3((-2x + 2)/(-1x + 3)) - 4 and g(x) = -2x - 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) = (2(3(-3|(1x^2 + 3x - 4) + 3| + 1) + 3) + 2)/(-1(3(-3|(1x^2 + 3x - 4) + 3| + 1) + 3) - 3) and g(x) = -5(-3cos(3π(-1x^2 - 2x - 5) - 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) = 1(1|((2(4x - 2) - 3)/(3(4x - 2) - 1)) - 2| - 1)^2 + 2(1|((2(4x - 2) - 3)/(3(4x - 2) - 1)) - 2| - 1) - 2 and g(x) = 3|(-3sin(2π(1x^2 + 5x - 5) - 1) - 1) + 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) = (-1(-3(-1|x + 3|) - 5) + 3)/(-3(-3(-1|x + 3|) - 5) - 3) and g(x) = (-1(-3|x - 2| + 2) - 2)/(-2(-3|x - 2| + 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(-2|x + 2|) + 2)/(3(-2|x + 2|) + 1) and g(x) = 3x + 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) = -1|(2e^(1(3x + 2)) + 2)| - 2 and g(x) = -5(2cos(1πx + 3) + 3)^2 + 5(2cos(1πx + 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) = 1|(2((1x)/(1x - 2))^2 - 5((1x)/(1x - 2)) + 2) + 3| - 3 and g(x) = -2cos(2π(-1|x + 3| - 2) + 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) = 4(2|(5((-1x)/(-1x - 1))^2 + 1((-1x)/(-1x - 1)) + 2) + 3| - 3) - 4 and g(x) = 2(3|(-4x - 1) - 3| + 2)^2 + 5(3|(-4x - 1) - 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) = 5(3cos(2π(2|((-3x - 1)/(-1x + 2)) + 1| + 3) - 1) + 1) + 2 and g(x) = -2(-1sin(1π(1|x + 2| + 3) - 2) - 2)^2 - 4(-1sin(1π(1|x + 2| + 3) - 2) - 2) - 5 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(-1|(2cos(1π(1x + 1) + 1) - 1)|)^2 - 1(-1|(2cos(1π(1x + 1) + 1) - 1)|) + 2 and g(x) = 3|(-2cos(2π((1x - 1)/(-3x - 2)) + 2) - 1) + 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(1π(-4((2x - 2)/(1x + 1))^2 - 2) + 1) - 2 and g(x) = -1(1sin(1πx - 2) - 1)^2 + 3(1sin(1πx - 2) - 1) + 1 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation 3(2|(-5((1x - 1)/(3x + 3)) - 4) + 2| - 2)^2 - 4(2|(-5((1x - 1)/(3x + 3)) - 4) + 2| - 2) + 3 = (-2(4(-2cos(1πx + 2) + 1) - 1) - 3)/(3(4(-2cos(1πx + 2) + 1) - 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) = 3(-3x^2 - 4x + 1) + 3 and g(x) = 2|x + 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) = -4(-2sin(2π(3x^2 + 3x - 2)) + 1) + 5 and g(x) = -1sin(2π(-1x - 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) = 2((2(-3e^(2(2x^2 - 5x + 1)) + 1))/(2(-3e^(2(2x^2 - 5x + 1)) + 1) + 3)) + 1 and g(x) = (-1(2(3cos(1πx - 2) - 1) + 2) + 2)/(-2(2(3cos(1πx - 2) - 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) = (3(-3sin(2π(-5x - 5) + 1) + 2) + 2)/(-2(-3sin(2π(-5x - 5) + 1) + 2) + 1) and g(x) = 1sin(2π(3|x - 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|(-4(4x^2 + 1x - 4) - 2) - 1| + 2 and g(x) = -3sin(3π(-1|x| - 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 1(-2sin(2πx))^2 - 3(-2sin(2πx)) + 4 = (2x - 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|(1sin(3π(-2(-4x - 2)^2 + 4(-4x - 2) - 4) + 3) + 1) - 3| - 1 = 2|(-3((2x + 1)/(-1x)) + 3) - 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 2(-3|((-2(4x^2 - 2x + 1) + 2)/(-1(4x^2 - 2x + 1) + 3)) + 3| - 1) - 2 = -2(5(1|x - 1| - 2) - 1)^2 + 2(5(1|x - 1| - 2) - 1) - 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) = 2(1|(4x + 4) + 2| - 1)^2 - 4(1|(4x + 4) + 2| - 1) - 2 and g(x) = -1(1e^(2x) - 1) - 4 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (-3(-1|(-1(5x - 4)^2 + 4(5x - 4) - 2) + 3| + 3) + 3)/(-1(-1|(-1(5x - 4)^2 + 4(5x - 4) - 2) + 3| + 3) + 2) = -1|((3(1cos(3πx + 2) - 2) + 1)/(1(1cos(3πx + 2) - 2) - 2)) + 2| + 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(3cos(1πx + 1)) - 1) - 3| - 3 and g(x) = 4(-1cos(2πx + 3) + 1)^2 + 1(-1cos(2πx + 3) + 1) - 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) = (-3(-4(-1x^2 + 5) - 2) + 2)/(1(-4(-1x^2 + 5) - 2)) and g(x) = -3|((1x + 2)/(-3x + 2)) - 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) = (-1(-1sin(1πx - 2) + 1) - 2)/(-1(-1sin(1πx - 2) + 1) + 2) and g(x) = -1|x - 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) = -1sin(3π(-1|x + 2| + 3) + 2) + 3 and g(x) = 3|x| - 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((1(-5x^2 + 5x + 4) - 3)/(2(-5x^2 + 5x + 4) - 1)) - 3 and g(x) = (3(-2cos(3πx + 3) + 1) - 2)/(-1(-2cos(3πx + 3) + 1) + 2) where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -2(-1sin(3π((-3(3|x| - 2) - 2)/(-1(3|x| - 2) - 3)) - 3))^2 - 5(-1sin(3π((-3(3|x| - 2) - 2)/(-1(3|x| - 2) - 3)) - 3)) + 1 = -2e^(1(-3|(2x - 1) + 2| - 3)) + 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 1((2x - 2)/(-3x + 2)) - 3 = (2x + 3)/(1x) 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((-2(2|(-2x^2 - 4x + 3) - 1|) + 2)/(2(2|(-2x^2 - 4x + 3) - 1|) - 1)) - 1 = -4(-1cos(2π((2x + 3)/(3x + 1)) + 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(3sin(1π(-1|x + 3| + 3) - 3) + 3) + 5 = (1(3x - 3) - 1)/(-2(3x - 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|(1((-3x)/(2x - 1))^2 + 2((-3x)/(2x - 1)) - 3) + 1| - 1 and g(x) = 3(3x)^2 + 5(3x) + 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) = -2cos(3π(2(-1|(-3x + 3) - 3| - 3)^2 - 2(-1|(-3x + 3) - 3| - 3) + 4) + 3) - 3 and g(x) = -1(4(1|x - 3| + 1)^2 - 4(1|x - 3| + 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(-2|(-1((3x + 3)/(1x + 2)) + 4)| + 2)^2 + 5(-2|(-1((3x + 3)/(1x + 2)) + 4)| + 2) and g(x) = 2e^(-1(-2(-3x^2 - 2x) + 1)) where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -2e^(-1(3(3x - 1)^2 + 1(3x - 1) + 2)) + 2 = 5(1|x - 2| + 1) - 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((2(-2(-1|x - 3|)^2 - 5(-1|x - 3|) + 2) + 2)/(-1(-2(-1|x - 3|)^2 - 5(-1|x - 3|) + 2))) - 5 and g(x) = -4((-1(3|x - 1| - 1))/(1(3|x - 1| - 1))) - 4 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -1((-3(-2|(-4x - 5) + 2| + 2) + 2)/(-2(-2|(-4x - 5) + 2| + 2) - 3))^2 - 4((-3(-2|(-4x - 5) + 2| + 2) + 2)/(-2(-2|(-4x - 5) + 2| + 2) - 3)) = -2|(-1(-2sin(2πx - 1) + 1) - 2) - 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) = (1(-2|(4x^2 + 1x + 1)| - 3) + 1)/(3(-2|(4x^2 + 1x + 1)| - 3) + 2) and g(x) = 3cos(1π((1x - 3)/(2x + 3)) + 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) = (-1(-4(2|x + 2| - 1)) + 1)/(3(-4(2|x + 2| - 1)) - 2) and g(x) = 3((3x + 2)/(-2x - 1)) in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 5(1(-1e^(-1x) + 1) - 2)^2 - 4(1(-1e^(-1x) + 1) - 2) + 5 = -5(-3|x - 3| - 1) - 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(5((2(2|x - 3| - 2))/(3(2|x - 3| - 2) + 1)) - 1)^2 + 5(5((2(2|x - 3| - 2))/(3(2|x - 3| - 2) + 1)) - 1) - 4 and g(x) = 3|(-3((2x - 1)/(-2x - 1))^2 + 2((2x - 1)/(-2x - 1))) + 2| - 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) = -5(-1|(-5((-3x)/(-2x - 3))^2 - 3((-3x)/(-2x - 3)) + 4) - 1|) + 4 and g(x) = 5((-2(4x + 2) - 2)/(-1(4x + 2) - 3))^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) = -1|((-2(-3x - 1) - 2)/(-2(-3x - 1) + 3)) - 2| and g(x) = -3|(3e^(2x) - 1) - 1| - 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) = 3|((2(3sin(2π(3x^2 + 5x + 1) + 3)) + 3)/(-1(3sin(2π(3x^2 + 5x + 1) + 3)) - 2)) + 2| + 3 and g(x) = 4(-3|(1x + 2) + 2| + 3)^2 - 5(-3|(1x + 2) + 2| + 3) + 4 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -1(3((-1(-2|x - 3| - 1) + 3)/(-3(-2|x - 3| - 1) + 2))^2 + 5((-1(-2|x - 3| - 1) + 3)/(-3(-2|x - 3| - 1) + 2)) + 3) + 2 = -4(2|(1x + 5) - 1| - 3)^2 - 4(2|(1x + 5) - 1| - 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) = -2(-3cos(2πx) + 2) - 4 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 points of intersection exist between the functions f(x) = (-3(2|(4x - 1) + 2| - 1) + 2)/(1(2|(4x - 1) + 2| - 1) - 2) and g(x) = (1(2e^(1x) + 1) - 3)/(1(2e^(1x) + 1) + 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) = (-3(3|(2x^2 + 4x + 3) - 2| + 3) - 3)/(1(3|(2x^2 + 4x + 3) - 2| + 3) - 3) and g(x) = 1(1e^(1x) - 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) = 2|(3sin(1π(3((-2x - 3)/(-3x + 2))^2 - 4((-2x - 3)/(-3x + 2)) - 3) - 2) + 2) - 3| - 1 and g(x) = 1((-1(4x - 4) + 2)/(3(4x - 4) - 2))^2 + 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(-3|x + 1| - 1) - 3)/(-3(-3|x + 1| - 1) - 3)) + 1 and g(x) = -2(1|x| - 1)^2 - 3(1|x| - 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) = 5((1(-2x^2 + 1x))/(1(-2x^2 + 1x) - 3)) - 3 and g(x) = (1(-1|x - 3| + 2))/(3(-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 5((2(-1e^(1x) - 1) + 3)/(2(-1e^(1x) - 1) - 1)) + 4 = 1|((-1x + 3)/(3x - 2)) + 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) = (-2(-5(3|(-3x - 1)| + 1)^2 - 2(3|(-3x - 1)| + 1) + 2) - 3)/(2(-5(3|(-3x - 1)| + 1)^2 - 2(3|(-3x - 1)| + 1) + 2) - 3) and g(x) = (-3(2(1x^2 + 4x - 5) + 1) - 1)/(-2(2(1x^2 + 4x - 5) + 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(2|x - 1| - 1) - 3 and g(x) = 1x^2 + 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) = (2(1x^2 - 1) - 2)/(-1(1x^2 - 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) = 2(-2|x|)^2 + 5(-2|x|) - 5 and g(x) = (-1x - 1)/(-2x + 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((1x - 1)/(1x + 2)) - 1 and g(x) = -1x intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation 1|(-5x^2 + 1x + 5) - 2| = -1x^2 + 3x + 5 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|(-3(5((-3x - 1)/(-2x)) + 5)^2 - 5(5((-3x - 1)/(-2x)) + 5) + 3) + 3| - 3 and g(x) = 2(4((-3x)/(2x - 3))^2 + 2((-3x)/(2x - 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) = -5(1cos(1πx + 2) + 1) - 2 and g(x) = 5x + 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) = (1(-2|x - 1| - 1) + 2)/(-2(-2|x - 1| - 1) + 3) and g(x) = 2|x - 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) = 2(-3x^2 + 4x + 5) + 5 and g(x) = (2x - 2)/(1x + 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) = (3(3(5x^2 + 5x - 1)))/(3(3(5x^2 + 5x - 1)) + 1) and g(x) = 3cos(2π(4x^2 - 5x - 3) + 2) + 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) = -2(-3(-3|x - 3| + 3)^2 + 5(-3|x - 3| + 3) - 1) - 2 and g(x) = 3(2sin(2πx - 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|(1(3x^2 + 4x) + 4) - 1| + 2 and g(x) = -2|(5x + 5) + 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) = 1sin(1π((-1(-1x - 5) + 2)/(-2(-1x - 5) + 3)) + 3) - 2 and g(x) = -2|(1x^2 - 2x - 4) - 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(5(2|x + 3| - 3)^2 + 1(2|x + 3| - 3) - 2) + 2 and g(x) = (-1(2e^(-1x) + 2) - 1)/(1(2e^(-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) = 1((-1(1(-2|x - 3| - 1) - 1) + 3)/(-3(1(-2|x - 3| - 1) - 1) + 4))^2 + 4((-1(1(-2|x - 3| - 1) - 1) + 3)/(-3(1(-2|x - 3| - 1) - 1) + 4)) - 4 and g(x) = 3cos(1π(3(-1|x - 2| - 3)^2 - 4(-1|x - 2| - 3) - 3) + 2) - 1 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -1cos(2π(-1|(-4x + 2) + 1| - 3) - 3) = 4((-2x - 2)/(-1x + 2))^2 + 4((-2x - 2)/(-1x + 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) = 1e^(1(-1x^2 - 4x - 2)) + 1 and g(x) = 1x^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) = 1((-1x - 3)/(1x - 2)) - 1 and g(x) = 3|x + 3| - 1 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -3sin(2π(-1|x| + 3) + 2) + 1 = (1x)/(-3x) 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|((2x - 3)/(3x - 2)) + 1| + 2 = (-2x + 1)/(-1x - 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) = -2cos(3π(3(4((-1x + 3)/(3x)) + 2)^2 + 3(4((-1x + 3)/(3x)) + 2) - 1) + 3) - 3 and g(x) = -2sin(1π((-1(2x - 3) + 2)/(1(2x - 3) + 3)) - 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) = 5(-1e^(-2(4x^2 + 1x - 4)) + 2) + 1 and g(x) = (-2(2cos(2πx - 1) + 2) - 1)/(-2(2cos(2πx - 1) + 2) - 1) where -10 ≤ x ≤ 10.

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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