Question

Find (f°g)(x) and (g°f)(x) for the given functions:

A) (f°g)(x) = -6x and (g°f)(x) = -3(2x^2 - 1)
B) (f°g)(x) = -6x and (g°f)(x) = -6x
C) (f°g)(x) = 6x and (g°f)(x) = 6x
D) (f°g)(x) = -6x^2 - 1 and (g°f)(x) = -3x

Answer 1

For (f°g)(x), substitute -6x into f(x) and simplify. For (g°f)(x), substitute -6x into g(x) and simplify.

Step-by-step explanation:

Given (f°g)(x) = -6x and (g°f)(x) = -3(2x^2 - 1)

(f°g)(x) is the composition of functions f and g, which is defined as f(g(x)). So, we substitute -6x into f(x) to get f(-6x) which simplifies to -6(-6x) = 36x.

(g°f)(x) is the composition of functions g and f, which is defined as g(f(x)). So, we substitute -6x into g(x) to get g(-6x) = -3(2(-6x)^2 - 1) = -3(2(36x^2) - 1) = -3(72x^2 - 1) = -216x^2 + 3.