Question

For the function h(x) defined below . Find the function f(x) and g(x)

Answer 1

1st option.

`f\left(x\right)=x^3\text{ and }g\left(x\right)=(x+2)/(x)`

Explanation:

We have the following composite function obtained from two functions:

`h(x)=\:\left(f\circ g\right)\left(x\right)=\left((x+2)/(x)\right)^3`

We can determine the functions as follows:

`\begin{gathered} \left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right) \\ \\ f\left(g\left(x\right)\right)=\left((x+2)/(x)\right)^3 \\ \\ g(x)=(x+2)/(x),\text{ therefore} \\ \\ f(x)=x^3 \end{gathered}`

Therefore, the correct answer is the 1st option.