Question

Perform the indicated operation
g(x)=x^3+5x and f(x)=2x-2
Find (g o f)(x)

Answer 1

g(f(x)) = 8x^3-24x^2+34x-18

Explanation:

The composition is ...

`(g\circ f)(x)=g(f(x))=g(2x-2)\\\\=(2x-2)^3+5(2x-2)\\\\=(2x)^3 +3(-2)(2x)^2+3(-2)^2(2x)+(-2)^3+10x-10\\\\=8x^3-24x^2 +24x-8+10x-10\\\\\boxed{(g\circ f)(x)=8x^3-24x^2+34x-18}`