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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


[User]
Determine the number of intersection points between the functions f(x) = -5(4(2sin(2πx + 3) + 1) + 2)^2 - 5(4(2sin(2πx + 3) + 1) + 2) and g(x) = 4((-1x + 2)/(-1x - 3))^2 - 3((-1x + 2)/(-1x - 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|(1e^(1((-3x + 1)/(-1x - 1))) - 1) - 2| - 3 and g(x) = -2|(-1x - 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 3(-1|(-2x + 1) + 3| + 2)^2 - 1(-1|(-2x + 1) + 3| + 2) + 4 = 2((-3x + 1)/(-2x)) + 3 have for x in the interval [-10, 10]?

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


[User]
Determine the number of intersection points between the functions f(x) = (-2(-2x - 2) - 3)/(-2(-2x - 2) + 3) and g(x) = 1x - 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(-1(-1x + 2)^2 - 4(-1x + 2) - 3) - 1)/(3(-1(-1x + 2)^2 - 4(-1x + 2) - 3) + 3)) - 3| and g(x) = 1|(-2(-1x^2 - 4x + 3) - 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) = 1(-2sin(3πx + 3)) - 2 and g(x) = -2|x - 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|((2(-3(-4x + 2)^2 - 3(-4x + 2) + 4) + 3)/(3(-3(-4x + 2)^2 - 3(-4x + 2) + 4) - 1))| = -2|(1(5x + 3)^2 + 3(5x + 3) - 1) + 1| + 1 have for x in the interval [-10, 10]?

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


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

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


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

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


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

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


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

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


[User]
Find the number of times the graphs of f(x) = 2(3|x| - 3) + 4 and g(x) = 1x + 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) = -3((1x + 1)/(1x + 3)) - 2 and g(x) = 2x + 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) = -1((-1(-4x - 4) + 3)/(-2(-4x - 4) - 3))^2 - 2((-1(-4x - 4) + 3)/(-2(-4x - 4) - 3)) - 1 and g(x) = -2|(3x + 3) + 3| - 2 in the range -10 ≤ x ≤ 10?

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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