Question

Function Decomposition

Given the composition h(x) = f(g(x))
If h(x) = (x + 5)8 and f(x) = x8, find the function g(x). Help!! I'm so confused!
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Answer 1

`g(x)=(x+5)`

Explanation:

we have

`h(x)=f(g(x))`

`f(x)=x^(8)`

`h(x)=(x+5)^(8)`

we know that

The variable of the function f(g(x)) is equal to the function g(x)

so

f(x) -----> f(g(x))

x^{8} -----> (x+5)^{8}

The variable x becomes (x+5)

therefore

The function g(x) is equal to

`g(x)=(x+5)`