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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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