Question

Given the definitions of f(x)f(x) and g(x)g(x) below, find the value of (f\circ g)(-4).(f∘g)(−4). f(x)= f(x)= \,\,3x^2+4x-3 3x 2 +4x−3 g(x)= g(x)= \,\,-2x-11 −2x−11

Answer 1

Answer:

(f∘g)(−4) = 12

Step-by-step explanation:

Given the functions

f(x)= 3x^2 + 4x - 3

g(x) = -2x-11

Required

(f∘g)(−4)

(f∘g)(x) = f(g(x))

f(g(x)) = f(-2x-11)

f(-2x-11) = 3(-2x-11)^2 + 4(-2x-11) - 3

f(g(x)) = 3(-2x-11)^2 + 4(-2x-11) - 3

f(g(-4)) = 3(-2(-4)-11)^2 + 4(-2(-4)-11) -3

f(g(-4)) = 3(8-11)^2 + 4(8-11) - 3

f(g(-4)) = 3(-3)^2 + 4(-3) - 3

f(g(-4))  = 3(9) - 12 - 3

f(g(-4))  = 27 - 15

f(g(-4)) = 12

Hence (f∘g)(−4) = 12