Express functions

Question

Express the function ℎ(x)=(x+9)^8 in the form f ∘ g. If f(x)=x^8, find the function g(x).

Your answer is g(x)=

Answer 1

Given that the function is f(x)=x^8.

To find the function g(x).

Also express the function h(x)=(x+9)^8 in the form of f o g.

Consider that the function g(x)=(x+9).

The composition rule of f o g is as follows.

f o g = f(g(x))

f o g = f(x+9)

f o g = (x+9)^8.

f o g = h(x).

Answer 2

g(x) = x + 9 and f(x) = x⁸

So, (f o g)(x) = f(g(x)) = f(x+9) = (x+9)⁸ = h(x)