Question

Given f(x), find g(x) and h(x) such that f(x)= g(h(x)) and neither g(x) nor h(x) is solely x.

Answer 1

Given:

`\begin{gathered} f(x)=g(h(x)) \\ f(x)=\sqrt[]{-4x^2-3}+2 \end{gathered}`

Solve :

`g(h(x)=\sqrt[]{-4x^2-3}+2`

The function g(x) convert then x is equal to h(x) then:

`\begin{gathered} h(x)=-4x^2 \\ g(x)=\sqrt[]{x-3}+2 \end{gathered}`