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

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dataset: MATH


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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


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

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

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

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


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

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

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


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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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