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 x^3 - 2. h(x)=\sqrt7{x^3 - 2} f(x)= (simplify your answer.)

Explanation:

Step1: Recall function - composition definition

The composition of two functions \(f\) and \(g\) is \((f\circ g)(x)=f(g(x))\). We are given that \(g(x)=x^{3}-2\) and \(h(x)=\sqrt[7]{x^{3}-2}\).

Step2: Identify \(f(x)\)

If \(g(x)=x^{3}-2\) and \(h(x) = f(g(x))=\sqrt[7]{x^{3}-2}\), then we can let \(f(x)=\sqrt[7]{x}\). When we substitute \(g(x)\) into \(f(x)\), we get \(f(g(x))=\sqrt[7]{g(x)}=\sqrt[7]{x^{3}-2}\), which is equal to \(h(x)\).

Answer:

\(f(x)=\sqrt[7]{x}\)