Split (1)

train · 1k rows

messages listlengths 1 1	ground_truth stringlengths 1 4	dataset stringclasses 1 value
[ { "content": "Find the number of times the graphs of f(x) = 1\|(-1((-2(1\|x + 1\| + 1) - 3)/(1(1\|x + 1\| + 1)))^2 + 4)\| + 1 and g(x) = (-1(2sin(1π(-4x^2 - 3x + 5) - 2) - 1) + 1)/(1(2sin(1π(-4x^2 - 3x + 5) - 2) - 1) + 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}...	379	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = -2sin(3π(-3(1\|(1\|x - 2\| - 1) - 2\|) + 1) - 2) + 2 and g(x) = 1\|(-3\|(-3x^2 + 2x + 5) - 1\| - 2) + 2\| - 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = -2(-5(-3\|(3x^2 - 1x - 5) + 3\| + 3) - 4) + 2 and g(x) = (3((3((1x - 1)/(-2x - 3)))/(-2((1x - 1)/(-2x - 3)) + 1)) - 2)/(-2((3((1x - 1)/(-2x - 3)))/(-2((1x - 1)/(-2x - 3)) + 1)) - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex form...	5	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = (2(4((-2(-1x^2 + 5x + 5) - 2)/(-3(-1x^2 + 5x + 5))) + 4) - 2)/(-1(4((-2(-1x^2 + 5x + 5) - 2)/(-3(-1x^2 + 5x + 5))) + 4) + 3) and g(x) = -5(-2(-5x - 5)^2 + 3)^2 + 5(-2(-5x - 5)^2 + 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the ans...	5	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = (-3(2cos(3π(5(3x^2 - 4x + 1)^2 + 2(3x^2 - 4x + 1) - 4) - 3) - 3) - 2)/(-1(2cos(3π(5(3x^2 - 4x + 1)^2 + 2(3x^2 - 4x + 1) - 4) - 3) - 3) - 3) and g(x) = (1(1sin(1π((-2x)/(-1x - 1))) + 2) - 3)/(1(1sin(1π((-2x)/(-1x - 1))) + 2)) in the...	260	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 2((3(1(2sin(3πx + 1) - 3) + 4) + 1)/(3(1(2sin(3πx + 1) - 3) + 4) - 2))^2 + 2((3(1(2sin(3πx + 1) - 3) + 4) + 1)/(3(1(2sin(3πx + 1) - 3) + 4) - 2)) + 5 and g(x) = 1(2(2e^(1x) - 1)^2 - 1(2e^(1x) - 1) + 3) where -10 ≤ x ≤ 10.\n\n...	65	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = (2(-4(-1(-2cos(2πx - 2))^2 + 4(-2cos(2πx - 2)) - 1)^2 + 1(-1(-2cos(2πx - 2))^2 + 4(-2cos(2πx - 2)) - 1) - 3) + 2)/(3(-4(-1(-2cos(2πx - 2))^2 + 4(-2cos(2πx - 2)) - 1)^2 + 1(-1(-2cos(2πx - 2))^2 + 4(-2cos(2πx - 2)) - 1) - 3) + 2) and...	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = -2(-1sin(3π(2\|(-1x^2 + 1x - 1) - 1\| - 3))) - 5 and g(x) = -3cos(2π((-1(1\|x\| + 2) + 1)/(1(1\|x\| + 2) - 3)) - 1) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	100	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 3\|(-1\|(1\|(-3\|x - 1\| - 3) + 2\|)\| - 3)\| + 2 and g(x) = 3(5((3x + 3)/(2x + 3))^2 + 2((3x + 3)/(2x + 3)) + 2) + 5 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = 2cos(2π(-1(-1\|(-2\|x + 1\| + 3) - 1\|)^2 + 4(-1\|(-2\|x + 1\| + 3) - 1\|) - 4) - 2) - 1 and g(x) = 1e^(-1((2(-2x) + 3)/(-3(-2x) + 4))) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	29	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 5(-5((-2(-1e^(-2x) + 3) - 2)/(-2(-1e^(-2x) + 3) - 3))^2 - 1((-2(-1e^(-2x) + 3) - 2)/(-2(-1e^(-2x) + 3) - 3)) + 4) + 4 and g(x) = -5(3\|(3sin(1πx + 1) - 1)\| + 2) + 4 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \...	7	MATH
[ { "content": "How many solutions does the equation 3\|(-3(-3(-2sin(1πx - 3) + 2)^2 + 2(-2sin(1πx - 3) + 2) + 4) + 4) - 1\| - 3 = 1cos(3π(-3(-3\|x - 3\| + 2)^2 - 3(-3\|x - 3\| + 2) + 2) + 3) - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	33	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = -2((3(3(2\|x + 3\| + 1)^2 - 5(2\|x + 3\| + 1) - 4) - 3)/(-3(3(2\|x + 3\| + 1)^2 - 5(2\|x + 3\| + 1) - 4)))^2 + 3((3(3(2\|x + 3\| + 1)^2 - 5(2\|x + 3\| + 1) - 4) - 3)/(-3(3(2\|x + 3\| + 1)^2 - 5(2\|x + 3\| + 1) - 4))) - 3 and g(x) = -1\|(-1cos(3π((-...	4	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = (-1(-2\|((-1(2x^2 + 4x - 4) - 1)/(3(2x^2 + 4x - 4) - 2)) - 2\| - 2) - 1)/(1(-2\|((-1(2x^2 + 4x - 4) - 1)/(3(2x^2 + 4x - 4) - 2)) - 2\| - 2) + 2) and g(x) = -5(-1(-3\|x + 1\| + 1)^2 - 5(-3\|x + 1\| + 1) + 3) + 4 in the range -10 ≤ x ≤ 10?\n...	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = 2(4(2e^(-2(3x^2 - 4x - 5)) - 3) - 4)^2 + 4(4(2e^(-2(3x^2 - 4x - 5)) - 3) - 4) + 1 and g(x) = 1\|(4(3\|x - 3\| - 1)^2 - 3(3\|x - 3\| - 1) - 5)\| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...	4	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 1(3(4(1x^2 + 3x - 2)^2 - 2(1x^2 + 3x - 2) - 4)^2 + 1) and g(x) = 1((-3(-1\|x\| + 1) + 3)/(-2(-1\|x\| + 1) + 3))^2 + 3((-3(-1\|x\| + 1) + 3)/(-2(-1\|x\| + 1) + 3)) + 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxe...	8	MATH
[ { "content": "How many solutions does the equation 4(5(2(3sin(2πx + 1) - 1) + 4)^2 - 4) + 1 = 1(-3cos(3π(-4x^2 + 5x - 1) + 1) - 3)^2 + 5(-3cos(3π(-4x^2 + 5x - 1) + 1) - 3) - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	90	MATH
[ { "content": "Find the number of times the graphs of f(x) = 3\|(4(-1\|(-3x^2 - 4x + 1) + 2\| + 1)^2 + 2(-1\|(-3x^2 - 4x + 1) + 2\| + 1) - 2) - 1\| + 3 and g(x) = 5((2(2cos(2πx) - 1) - 2)/(3(2cos(2πx) - 1) - 1)) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...	9	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = -3sin(1π(-1\|(-5(4x^2 + 4x + 2) + 1) - 3\| + 1) - 2) - 1 and g(x) = 3\|(-1\|(-1\|x\| - 2) + 3\| + 2) - 1\| in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	185	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 3((1((-3(2\|x + 2\| - 2) + 1)/(2(2\|x + 2\| - 2) + 3)) + 2)/(1((-3(2\|x + 2\| - 2) + 1)/(2(2\|x + 2\| - 2) + 3)))) - 4 and g(x) = 1sin(3π(3((-1x + 1)/(-2x - 3)) + 4) + 2) - 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format...	23	MATH
[ { "content": "How many solutions does the equation 3\|(1e^(1((3((-2x + 2)/(-1x - 3)))/(2((-2x + 2)/(-1x - 3)) + 3))) - 3) - 3\| + 3 = 2\|(3(2\|x - 1\| - 2)^2 - 3(2\|x - 1\| - 2) + 1)\| have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "How many solutions does the equation -5(3sin(1π(-1(2\|x\| - 3)^2 - 4(2\|x\| - 3) + 1) + 2))^2 + 2(3sin(1π(-1(2\|x\| - 3)^2 - 4(2\|x\| - 3) + 1) + 2)) + 5 = -5(2cos(3π(-3\|x + 3\| + 3) + 3) - 1)^2 - 3(2cos(3π(-3\|x + 3\| + 3) + 3) - 1) + 5 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex fo...	952	MATH
[ { "content": "How many solutions does the equation -1\|((3(-1(-2cos(1πx - 1) + 1)) + 1)/(-3(-1(-2cos(1πx - 1) + 1)) + 2)) - 3\| - 1 = -1\|(-1\|(1cos(2πx + 2) - 3) + 3\| + 3)\| - 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	20	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 4(-1(4(-2\|x + 3\| + 3) + 4)^2 + 2(4(-2\|x + 3\| + 3) + 4) + 5) - 4 and g(x) = 2(3(5x^2 + 4x - 3)^2 - 1(5x^2 + 4x - 3) - 3)^2 + 1(3(5x^2 + 4x - 3)^2 - 1(5x^2 + 4x - 3) - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex f...	4	MATH
[ { "content": "How many solutions does the equation -3sin(3π(-5(3\|(-1x - 1) - 3\|) + 3)) - 3 = -1((2(1cos(3πx - 2)) - 1)/(-2(1cos(3πx - 2)) - 1))^2 - 3((2(1cos(3πx - 2)) - 1)/(-2(1cos(3πx - 2)) - 1)) + 5 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...	120	MATH
[ { "content": "How many solutions does the equation -1(5(-4(2sin(3πx + 3) - 2)^2 - 1(2sin(3πx + 3) - 2)))^2 - 1(5(-4(2sin(3πx + 3) - 2)^2 - 1(2sin(3πx + 3) - 2))) + 2 = 2(1sin(3π(-5x^2 - 1x + 3) + 2) + 1) - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...	349	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 2(-1((-1(-2sin(1πx - 2)) + 1)/(3(-2sin(1πx - 2)) + 3))^2 + 3((-1(-2sin(1πx - 2)) + 1)/(3(-2sin(1πx - 2)) + 3)) - 2) - 1 and g(x) = (-2(-3sin(3π(-5x^2 + 1x + 5) + 3) + 1) - 3)/(2(-3sin(3π(-5x^2 + 1x + 5) + 3) + 1)) where -10 ≤...	276	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = (-2(1((2(1cos(2πx + 1) + 1) - 3)/(2(1cos(2πx + 1) + 1) + 2)) - 2) - 2)/(-1(1((2(1cos(2πx + 1) + 1) - 3)/(2(1cos(2πx + 1) + 1) + 2)) - 2) - 2) and g(x) = (3(2cos(3π(-2\|x + 2\| + 1) + 1) - 1) + 2)/(-3(2cos(3π(-2\|x + 2\| + 1) + 1)...	65	MATH
[ { "content": "How many solutions does the equation 3((2(1((3x + 2)/(-2x + 3)) + 2))/(1(1((3x + 2)/(-2x + 3)) + 2) + 3))^2 - 5((2(1((3x + 2)/(-2x + 3)) + 2))/(1(1((3x + 2)/(-2x + 3)) + 2) + 3)) - 2 = 1\|(2sin(3π(-2x + 5) - 3) - 3) + 2\| - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex forma...	36	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 3cos(2π(4(-3(1x^2 - 2x - 3) + 5) - 3) + 1) - 3 and g(x) = -2e^(-2(5(-2x^2 + 4x - 4)^2 - 5(-2x^2 + 4x - 4) + 1)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1236	MATH
[ { "content": "Find the number of times the graphs of f(x) = 2sin(2π(1(3(1\|x + 2\| - 3) - 3)^2 - 2(3(1\|x + 2\| - 3) - 3) + 2) - 3) + 1 and g(x) = -4(-5((-2x - 2)/(-2x - 1)) + 3) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	28	MATH
[ { "content": "Find the number of times the graphs of f(x) = 2sin(2π(2(-3((1x + 3)/(2x - 3)) - 1) + 4) + 3) + 2 and g(x) = -5(-3((-3x - 2)/(-3x))^2 + 4((-3x - 2)/(-3x)) - 1) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "How many solutions does the equation (1(-2\|(2\|(2x + 5) + 1\| - 3) + 2\| - 1) - 2)/(2(-2\|(2\|(2x + 5) + 1\| - 3) + 2\| - 1) + 3) = 2e^(2(-1\|(2x - 3) + 1\| - 1)) + 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -1((-3(-3(-3\|x - 2\| + 2) + 4) + 1)/(-1(-3(-3\|x - 2\| + 2) + 4)))^2 + 5((-3(-3(-3\|x - 2\| + 2) + 4) + 1)/(-1(-3(-3\|x - 2\| + 2) + 4))) and g(x) = 3(4(-4x^2 + 5x - 1)^2 - 3(-4x^2 + 5x - 1) - 3)^2 - 2(4(-4x^2 + 5x - 1)^2 - 3(-4x^2 ...	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = 4((-1(2(-1\|x\| + 2) + 1) - 3)/(-2(2(-1\|x\| + 2) + 1) + 3)) - 1 and g(x) = -1cos(1π((1(-2\|x + 2\| + 3) - 3)/(-1(-2\|x + 2\| + 3) - 2))) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...	54	MATH
[ { "content": "Find the number of times the graphs of f(x) = -2\|(-3((-2(3\|x\| + 2))/(-2(3\|x\| + 2) - 1))^2 + 4((-2(3\|x\| + 2))/(-2(3\|x\| + 2) - 1)) - 2) - 1\| - 3 and g(x) = -1e^(1(2\|(2\|x + 3\| - 3) - 3\| - 1)) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = 2(-1\|(4(-2cos(1πx - 3) + 3)^2 + 1(-2cos(1πx - 3) + 3)) - 1\| + 2) - 5 and g(x) = -3\|((2(-1x) + 2)/(1(-1x) + 1)) + 1\| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	20	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 5(2sin(2π(5(3x + 3)^2 + 2(3x + 3) - 5) - 3) - 2)^2 + 1(2sin(2π(5(3x + 3)^2 + 2(3x + 3) - 5) - 3) - 2) - 5 and g(x) = -1\|(-5(-2\|x + 3\| + 3) - 5)\| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answ...	155	MATH
[ { "content": "Find the number of times the graphs of f(x) = (2((-2(2\|((3x)/(-1x + 2)) + 2\| + 1) + 2)/(3(2\|((3x)/(-1x + 2)) + 2\| + 1) + 3)))/(3((-2(2\|((3x)/(-1x + 2)) + 2\| + 1) + 2)/(3(2\|((3x)/(-1x + 2)) + 2\| + 1) + 3)) + 1) and g(x) = 2cos(1π(2((-1x + 2)/(1x + 2)) - 3) - 1) + 3 intersect in the interval [-10, 1...	6	MATH
[ { "content": "Find the number of times the graphs of f(x) = -3\|(3(-4(-2\|x + 2\| + 1)^2 - 1(-2\|x + 2\| + 1) + 4) + 2) - 2\| - 1 and g(x) = -2e^(-1((2(2\|x + 1\|) + 1)/(-2(2\|x + 1\|) - 3))) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 1(-1(-5((2x)/(-3x + 1)) + 2))^2 - 4(-1(-5((2x)/(-3x + 1)) + 2)) - 4 and g(x) = 2\|(-1(-4x^2 - 5x + 2) + 4) - 1\| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "How many solutions does the equation 4(4(-4(-3\|x + 1\| + 2)^2 - 4(-3\|x + 1\| + 2) + 1)^2 + 2(-4(-3\|x + 1\| + 2)^2 - 4(-3\|x + 1\| + 2) + 1) + 1)^2 - 5(4(-4(-3\|x + 1\| + 2)^2 - 4(-3\|x + 1\| + 2) + 1)^2 + 2(-4(-3\|x + 1\| + 2)^2 - 4(-3\|x + 1\| + 2) + 1) + 1) = 3\|((1(-3x + 1) + 3)/(-2(-3x + 1) + 3)) + 3\| + 1 h...	9	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = (-3(-1cos(2π((2(3x - 1) - 1)/(2(3x - 1) + 1)) + 1) - 1) - 2)/(-2(-1cos(2π((2(3x - 1) - 1)/(2(3x - 1) + 1)) + 1) - 1) - 2) and g(x) = 3(-3\|(1x + 5) + 2\| - 3) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\box...	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = (-2(2sin(3π(-4(-1x^2 - 2x + 2) - 5) + 1) - 1) - 1)/(1(2sin(3π(-4(-1x^2 - 2x + 2) - 5) + 1) - 1)) and g(x) = 1\|(1sin(2π((-1x - 2)/(2x - 1)) - 2) - 1)\| + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...	305	MATH
[ { "content": "Find the number of times the graphs of f(x) = (3(-2sin(3π((1((-3x - 2)/(-2x)) + 2)/(-2((-3x - 2)/(-2x)) - 2)) - 1)) - 3)/(-2(-2sin(3π((1((-3x - 2)/(-2x)) + 2)/(-2((-3x - 2)/(-2x)) - 2)) - 1))) and g(x) = -3(-1(2cos(3πx) + 2) - 3)^2 - 4(-1(2cos(3πx) + 2) - 3) + 5 intersect in the interval [-10, 10]...	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = 1\|(-3\|((-1(2cos(1πx) + 3) + 1)/(1(2cos(1πx) + 3) + 1)) - 1\| + 1) - 3\| + 2 and g(x) = 1((-2(-1sin(2πx + 2) - 1) + 2)/(-2(-1sin(2πx + 2) - 1) + 1))^2 + 2((-2(-1sin(2πx + 2) - 1) + 2)/(-2(-1sin(2πx + 2) - 1) + 1)) + 2 intersect in the interval [-10, 10].\...	40	MATH
[ { "content": "How many solutions does the equation (1(-1cos(2π(-2(-4x^2 - 2x + 3) - 1) - 2) + 3) - 2)/(-2(-1cos(2π(-2(-4x^2 - 2x + 3) - 1) - 2) + 3) - 1) = -2(3(-4x)^2 - 3(-4x) - 3)^2 - 5(3(-4x)^2 - 3(-4x) - 3) + 4 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}...	4	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 3(1((-2(3sin(3πx + 1)) + 1)/(2(3sin(3πx + 1)) + 3)) - 1)^2 - 1(1((-2(3sin(3πx + 1)) + 1)/(2(3sin(3πx + 1)) + 3)) - 1) - 4 and g(x) = 3sin(2π(4((-1x + 1)/(-2x - 1))^2 + 5((-1x + 1)/(-2x - 1)) - 2) - 3) + 2 where -10 ≤ x ≤ 10.\...	141	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 4(2(-3((1x + 1)/(-1x - 2))^2 - 1((1x + 1)/(-1x - 2)) + 4)^2 - 2) - 2 and g(x) = 1(-2(-3sin(3πx + 1) + 1) - 3)^2 - 5(-2(-3sin(3πx + 1) + 1) - 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answe...	50	MATH
[ { "content": "Find the number of times the graphs of f(x) = -1sin(2π(-1((1(1\|x - 2\| + 1) + 3)/(-2(1\|x - 2\| + 1) - 3))^2 + 5((1(1\|x - 2\| + 1) + 3)/(-2(1\|x - 2\| + 1) - 3)) + 3) + 2) - 3 and g(x) = 1sin(1π((2((-1x + 3)/(-1x + 2)) + 2)/(2((-1x + 3)/(-1x + 2)) - 1)) - 3) - 2 intersect in the interval [-10, 10].\n\nP...	50	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 4(3(1(-3\|x - 2\|) + 5)^2 + 2(1(-3\|x - 2\|) + 5) - 3) + 1 and g(x) = 1e^(-2(1\|(-2\|x - 3\| + 1) - 3\| + 2)) - 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 4(1cos(2π(-5(-1x^2 + 1x + 4)^2 - 5) + 2) + 2)^2 + 5 and g(x) = 2(3cos(1π(-1x - 3) + 3) - 1)^2 - 2(3cos(1π(-1x - 3) + 3) - 1) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...	386	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = -3cos(2π((1(3\|(5x + 5) - 2\| - 1) + 3)/(-3(3\|(5x + 5) - 2\| - 1) + 1)) + 2) + 1 and g(x) = (-1(-3(-5x + 1)^2 + 4(-5x + 1) - 3) + 3)/(1(-3(-5x + 1)^2 + 4(-5x + 1) - 3) + 2) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex for...	23	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = -2sin(2π((2(3\|(3x - 1)\| + 3) + 2)/(1(3\|(3x - 1)\| + 3) + 2)) + 1) - 1 and g(x) = 1sin(1π(5((1x - 3)/(1x - 2))) - 1) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 3sin(1π(2(-5((-3x + 2)/(-1x - 1)) - 5) + 2) + 3) + 2 and g(x) = -2((1(-4x - 5) + 2)/(3(-4x - 5) + 2)) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = -2(3cos(2π(5((-3x - 1)/(-1x - 2))^2 - 2((-3x - 1)/(-1x - 2)) + 4) + 3) - 1)^2 - 4(3cos(2π(5((-3x - 1)/(-1x - 2))^2 - 2((-3x - 1)/(-1x - 2)) + 4) + 3) - 1) + 2 and g(x) = (2(-3(-4x^2 - 3x + 5)^2 - 1(-4x^2 - 3x + 5) - 5) + 2)/(-3(-3(-4x^2 - 3x + 5)^2 - 1...	605	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = (-2(-5((-2((3x + 1)/(-3x + 1)) - 1)/(-3((3x + 1)/(-3x + 1)) + 2)) - 3) + 1)/(1(-5((-2((3x + 1)/(-3x + 1)) - 1)/(-3((3x + 1)/(-3x + 1)) + 2)) - 3) - 3) and g(x) = -1(3\|((2x + 1)/(2x - 1)) + 2\| - 2)^2 + 5(3\|((2x + 1)/(2x - 1)) + 2\| -...	5	MATH
[ { "content": "Find the number of times the graphs of f(x) = 2\|(1cos(2π(3\|((2x - 1)/(1x - 2)) - 1\| + 2) - 3)) + 2\| + 2 and g(x) = 4(4(-1\|x\| + 2) + 1)^2 - 2(4(-1\|x\| + 2) + 1) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	29	MATH
[ { "content": "Find the number of times the graphs of f(x) = (-2(3cos(2π(-5(5x + 2) - 1) + 3) + 2) + 2)/(2(3cos(2π(-5(5x + 2) - 1) + 3) + 2) - 1) and g(x) = 1cos(2π(-1((1x - 1)/(1x - 3)) + 1) - 1) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...	287	MATH
[ { "content": "How many solutions does the equation (-1(1\|((2(-2\|x + 2\| + 2) - 2)/(-3(-2\|x + 2\| + 2) - 3)) + 3\| + 1) + 2)/(-1(1\|((2(-2\|x + 2\| + 2) - 2)/(-3(-2\|x + 2\| + 2) - 3)) + 3\| + 1) + 2) = (-1(1cos(3π(-1\|x + 2\| + 2) + 2) - 2))/(2(1cos(3π(-1\|x + 2\| + 2) + 2) - 2) + 3) have for x in the interval [-10, 10]?\n\...	30	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -3cos(3π(3(-2\|(1x + 1) + 1\| + 2)^2 - 4(-2\|(1x + 1) + 1\| + 2) - 1) - 1) and g(x) = 5((-1(3x^2 - 5x + 2) + 1)/(-2(3x^2 - 5x + 2) - 2))^2 + 5((-1(3x^2 - 5x + 2) + 1)/(-2(3x^2 - 5x + 2) - 2)) - 2 where -10 ≤ x ≤ 10.\n\nPresent th...	1247	MATH
[ { "content": "How many solutions does the equation (-2((3((-1(-2x - 2))/(-1(-2x - 2) + 3)) - 2)/(-1((-1(-2x - 2))/(-1(-2x - 2) + 3)) + 3)))/(-3((3((-1(-2x - 2))/(-1(-2x - 2) + 3)) - 2)/(-1((-1(-2x - 2))/(-1(-2x - 2) + 3)) + 3)) - 2) = (1(2cos(1π(-3\|x\| - 3) + 1) - 1) - 2)/(3(2cos(1π(-3\|x\| - 3) + 1) - 1) - 2) hav...	17	MATH
[ { "content": "Find the number of times the graphs of f(x) = 3(-4((-2(1x^2 - 3x + 1) + 3)/(2(1x^2 - 3x + 1) + 3)) + 3) + 4 and g(x) = (-3(-4(-3cos(1πx - 2)) + 4))/(2(-4(-3cos(1πx - 2)) + 4) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...	6	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -2\|(-3\|(4(3\|x\| - 2) - 3) + 3\| + 1) - 2\| and g(x) = 5(-4(-1cos(2πx + 2) + 2)^2 - 5(-1cos(2πx + 2) + 2)) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -1\|(4(-1(3cos(1πx - 3) + 1) + 2)^2 + 5(-1(3cos(1πx - 3) + 1) + 2) - 1) - 1\| - 2 and g(x) = -5(2\|(2\|x - 3\| - 2) - 2\| + 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...	16	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 3(-1(-4(-1\|x\| + 2)^2 + 1(-1\|x\| + 2) + 1)^2 - 5(-4(-1\|x\| + 2)^2 + 1(-1\|x\| + 2) + 1) - 3) + 5 and g(x) = 1(-2sin(3π(-3x - 3) - 1) - 1) + 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...	8	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -2\|((2((-3((-3x - 2)/(-2x - 3)) + 2)/(-2((-3x - 2)/(-2x - 3)) + 3)))/(-1((-3((-3x - 2)/(-2x - 3)) + 2)/(-2((-3x - 2)/(-2x - 3)) + 3)) + 3)) + 2\| + 1 and g(x) = -3sin(1π(-3\|(-1\|x + 2\| - 2) - 1\| - 1) - 1) - 1 where -10 ≤ x ≤ 10...	46	MATH
[ { "content": "How many solutions does the equation (-3((1(2(1x^2 + 3x + 3)^2 + 3(1x^2 + 3x + 3)) - 3)/(-2(2(1x^2 + 3x + 3)^2 + 3(1x^2 + 3x + 3)) + 1)) - 2)/(2((1(2(1x^2 + 3x + 3)^2 + 3(1x^2 + 3x + 3)) - 3)/(-2(2(1x^2 + 3x + 3)^2 + 3(1x^2 + 3x + 3)) + 1)) + 3) = -3\|(2\|(-1x^2 + 5x + 3)\| - 1) - 2\| + 2 have for x i...	8	MATH
[ { "content": "How many solutions does the equation 3(2e^(-1(-2\|(5x - 5) - 1\| + 2)) - 2)^2 - 5(2e^(-1(-2\|(5x - 5) - 1\| + 2)) - 2) - 5 = 3\|(-3(2\|x - 3\| - 2) + 5) - 2\| have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "How many solutions does the equation -2(1\|(-1(-1x^2 + 2x + 5) + 1) - 3\|) - 3 = -4((-2(-4x))/(-2(-4x) + 3)) - 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "How many solutions does the equation 2sin(1π(-2((2(4x^2 - 3x - 1) - 3)/(1(4x^2 - 3x - 1) - 3))^2 + 5) + 2) - 3 = 4((-2(-3cos(2πx - 2)) - 1)/(-3(-3cos(2πx - 2)))) + 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	39	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 3cos(1π(-3(-2\|(2x - 1) + 2\| - 3) + 5) - 3) + 2 and g(x) = (-1(-1(-1x^2 + 5x + 3)^2 - 3(-1x^2 + 5x + 3) + 5) + 3)/(-2(-1(-1x^2 + 5x + 3)^2 - 3(-1x^2 + 5x + 3) + 5) - 3) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex forma...	242	MATH
[ { "content": "Find the number of times the graphs of f(x) = -1(2cos(1π(-1(-5x + 4) + 3)) + 1)^2 - 4(2cos(1π(-1(-5x + 4) + 3)) + 1) + 4 and g(x) = 1\|(-1(3e^(-2x) - 3)^2 + 1(3e^(-2x) - 3) - 4)\| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...	4	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -2((-2(2(2x^2 - 3x - 1) + 1) - 1)/(3(2(2x^2 - 3x - 1) + 1) + 2))^2 - 4((-2(2(2x^2 - 3x - 1) + 1) - 1)/(3(2(2x^2 - 3x - 1) + 1) + 2)) - 2 and g(x) = -2((2(2x^2 - 1x + 2) + 3)/(2(2x^2 - 1x + 2) + 1)) + 2 where -10 ≤ x ≤ 10.\n\n...	4	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -1\|(-4(1(2\|x - 3\| - 3) + 3)^2 - 3(1(2\|x - 3\| - 3) + 3) + 2)\| - 3 and g(x) = -1cos(3π(1(2x^2 - 2x - 3) + 3) - 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -1(2cos(3π((-2(-1\|x\| + 1) + 2)/(3(-1\|x\| + 1) + 3)) + 2)) - 3 and g(x) = 1(-3cos(3π((-1x + 3)/(-2x + 1))) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	59	MATH
[ { "content": "How many solutions does the equation 1\|(-2(-1cos(1π(1x^2 - 4x - 4) + 1) - 2) + 1) + 1\| + 1 = (2(5(-2cos(1πx - 2) - 1) - 3) + 1)/(2(5(-2cos(1πx - 2) - 1) - 3) + 3) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	20	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = (1((2(-1\|(-4x)\| + 1) - 3)/(-2(-1\|(-4x)\| + 1) + 1)) + 2)/(-3((2(-1\|(-4x)\| + 1) - 3)/(-2(-1\|(-4x)\| + 1) + 1)) - 1) and g(x) = 2((3(1x^2 + 1x - 5) + 3)/(2(1x^2 + 1x - 5) - 3))^2 + 3((3(1x^2 + 1x - 5) + 3)/(2(1x^2 + 1x - 5) - 3))...	4	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = (-2(3cos(3π((-1(-3x^2 + 1x - 2) - 3)/(1(-3x^2 + 1x - 2))) - 2) - 1))/(1(3cos(3π((-1(-3x^2 + 1x - 2) - 3)/(1(-3x^2 + 1x - 2))) - 2) - 1) + 1) and g(x) = -2sin(2π((2(1x^2 + 2x + 3) + 1)/(-1(1x^2 + 2x + 3)))) + 1 in the range -10 ≤ x ...	10	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 1\|((2(-3\|(3x - 1) + 3\| - 3) + 1)/(-1(-3\|(3x - 1) + 3\| - 3) + 3)) - 1\| + 2 and g(x) = 3sin(2π(-1\|(1\|x + 2\| + 2) + 1\| + 3) - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...	40	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 3\|(1(-3\|(-3x - 3) - 1\|)^2 + 5(-3\|(-3x - 3) - 1\|) - 1) - 1\| and g(x) = -2e^(-2(-1(1x^2 + 4x - 4) - 2)) + 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 1\|(-2e^(2((-3(2x - 2) - 2)/(1(2x - 2)))) + 1)\| + 3 and g(x) = (3(-3\|(-3e^(-1x) + 2) + 1\| - 2) - 2)/(1(-3\|(-3e^(-1x) + 2) + 1\| - 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...	4	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = (-2(-1(3\|(3\|x - 2\| - 3) - 1\| - 1) - 1) + 2)/(-2(-1(3\|(3\|x - 2\| - 3) - 1\| - 1) - 1) - 2) and g(x) = 1(3(-2\|x + 1\| + 2)^2 + 5(-2\|x + 1\| + 2) + 3) - 4 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answ...	6	MATH
[ { "content": "Find the number of times the graphs of f(x) = -5(5((1(-2cos(2πx - 2) - 2) - 2)/(-1(-2cos(2πx - 2) - 2) - 3)) + 3) - 4 and g(x) = -2(-2\|(-2e^(-2x) + 2) - 1\| + 1) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -1sin(3π(-4(-3(-4x - 5) + 2)^2 + 4(-3(-4x - 5) + 2) - 5) + 1) - 3 and g(x) = (-2(1(5x - 5)^2 - 3(5x - 5) - 2) - 3)/(1(1(5x - 5)^2 - 3(5x - 5) - 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answe...	250	MATH
[ { "content": "How many solutions does the equation -3cos(2π((2(-1((2x + 2)/(-1x - 3))^2 + 1((2x + 2)/(-1x - 3))) + 2)/(-2(-1((2x + 2)/(-1x - 3))^2 + 1((2x + 2)/(-1x - 3))))) - 3) + 2 = -1(2((2x + 2)/(-1x + 3))^2 - 4) - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your a...	73	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 2((-2(5(-1x^2 + 5x) + 5) + 1)/(1(5(-1x^2 + 5x) + 5) - 2))^2 - 5((-2(5(-1x^2 + 5x) + 5) + 1)/(1(5(-1x^2 + 5x) + 5) - 2)) - 1 and g(x) = (-2(1(4x + 3) + 3) - 1)/(-3(1(4x + 3) + 3) - 1) in the range -10 ≤ x ≤ 10?\n\nPresent the answer...	5	MATH
[ { "content": "How many solutions does the equation -2\|(2cos(1π(-1\|(2x^2) - 2\|) - 3) - 1) - 1\| - 1 = -4(-1sin(1π((-1x)/(1x - 2)) - 2) - 3)^2 - 5(-1sin(1π((-1x)/(1x - 2)) - 2) - 3) - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	31	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 1((-2(-1\|((-2x)/(-1x - 2)) - 2\| + 1) - 3)/(1(-1\|((-2x)/(-1x - 2)) - 2\| + 1)))^2 + 1((-2(-1\|((-2x)/(-1x - 2)) - 2\| + 1) - 3)/(1(-1\|((-2x)/(-1x - 2)) - 2\| + 1))) - 2 and g(x) = -2\|(1((2x + 3)/(-3x - 1)) + 2) - 3\| + 2 in the range -10...	4	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = (3(3(-4((-1x - 1)/(-3x - 1)) + 5) - 4) + 2)/(2(3(-4((-1x - 1)/(-3x - 1)) + 5) - 4) + 3) and g(x) = -2cos(2π(-1(1x - 3) - 1)) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...	41	MATH
[ { "content": "Find the number of times the graphs of f(x) = 4(5(5(1\|x + 3\| - 3) - 3)^2 + 1(5(1\|x + 3\| - 3) - 3) - 1) - 4 and g(x) = -3(1(-1cos(3πx + 1) - 1) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = -3\|((3(2sin(2π(-3x) + 1) + 2) - 1)/(-1(2sin(2π(-3x) + 1) + 2))) + 2\| - 3 and g(x) = -2(-3\|((-3x + 3)/(3x + 3)) - 3\| + 2)^2 - 3(-3\|((-3x + 3)/(3x + 3)) - 3\| + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \...	118	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 1(-4((3(2x^2 + 3x - 4) - 1)/(2(2x^2 + 3x - 4) + 1))^2 + 1((3(2x^2 + 3x - 4) - 1)/(2(2x^2 + 3x - 4) + 1)) + 1) + 5 and g(x) = -3cos(1π(-2(-1x^2 - 3x - 4) + 1)) + 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\...	18	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 1(-1(-2\|(1\|x + 2\| - 3) - 1\| + 3)^2 + 5(-2\|(1\|x + 2\| - 3) - 1\| + 3) + 3)^2 + 4(-1(-2\|(1\|x + 2\| - 3) - 1\| + 3)^2 + 5(-2\|(1\|x + 2\| - 3) - 1\| + 3) + 3) - 1 and g(x) = 4(-3\|(2sin(1πx + 2) - 1)\| + 1)^2 + 3(-3\|(2sin(1πx + 2) - 1)\| + 1) in...	20	MATH
[ { "content": "How many solutions does the equation 3\|(-5(3(-1x + 3) - 2)^2 + 1(3(-1x + 3) - 2) + 3) + 2\| + 1 = 2(1\|(2x^2 - 5x - 1) - 2\|) - 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = 1cos(3π((2(2\|(-1\|x\| - 3) - 3\| + 2) + 3)/(1(2\|(-1\|x\| - 3) - 3\| + 2) - 2)) + 1) + 3 and g(x) = -4(-1(-2\|x + 2\| - 1) - 4)^2 + 1(-1(-2\|x + 2\| - 1) - 4) + 5 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your ...	4	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = -5(-3((2(-2sin(2πx - 3) + 3) - 2)/(2(-2sin(2πx - 3) + 3) - 1))^2 - 1((2(-2sin(2πx - 3) + 3) - 2)/(2(-2sin(2πx - 3) + 3) - 1)) + 2)^2 + 1(-3((2(-2sin(2πx - 3) + 3) - 2)/(2(-2sin(2πx - 3) + 3) - 1))^2 - 1((2(-2sin(2πx - 3) + 3) - 2)/...	68	MATH
[ { "content": "Determine the number of intersection points between the functions f(x) = 1\|(4(5(2x) + 4) + 2) + 1\| + 1 and g(x) = 1(1\|(2x)\| + 2)^2 + 2(1\|(2x)\| + 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Find the number of times the graphs of f(x) = (-1(2cos(3π(-3(4x^2 - 1x - 3)^2 - 5(4x^2 - 1x - 3) + 5) - 1) + 1) - 3)/(-2(2cos(3π(-3(4x^2 - 1x - 3)^2 - 5(4x^2 - 1x - 3) + 5) - 1) + 1) + 3) and g(x) = -1\|(1sin(3π(1x^2 + 4x) + 3) + 2) - 1\| + 3 intersect in the interval [-10, 10].\n\nPresent the answe...	169	MATH
[ { "content": "How many points of intersection exist between the functions f(x) = -2\|(-2(-1\|(-2\|x + 3\|) - 1\| - 3) + 5) + 1\| - 2 and g(x) = -3e^(2(3\|(4x^2 - 1x - 4)\| - 1)) - 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.