Question

express the given function h as a composition of two functions f and g so that h(x)=(f ∘ g)(x), where one of the functions is 2x - 8. h(x)=(2x - 8)^9 f(x)=□

Explanation:

Step1: Identify the inner - function

Let \(g(x)=2x - 8\) as given.

Step2: Determine the outer - function

Since \(h(x)=(2x - 8)^9\) and \(g(x)=2x - 8\), then \(f(x)=x^9\) so that \((f\circ g)(x)=f(g(x))=f(2x - 8)=(2x - 8)^9=h(x)\)

Answer:

\(f(x)=x^9\)