Question

If h(x)=(fog)(x) and h(x)=³√x+3, find g(x) if f(x) =³√x+2

Answer 1

`g(x)=x+1`

The problem:

Find
`g(x)` if
`h(x)=(f \circ g)(x)`,

`h(x)=\sqrt[3]{x+3}`, and

`f(x)=\sqrt[3]{x+2}`.

Explanation:

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

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

Replace
`x` in
`f(x)=\sqrt[3]{x+2}` with
`g(x)` since we are asked to find
`f(g(x))`:

`\sqrt[3]{x+3}=\sqrt[3]{g(x)+2}`

`\sqrt[3]{x+1+2}=\sqrt[3]{g(x)+2}`

This implies that
`x+1=g(x)`

Let's check:

`(f \circ g)(x)`

`f(g(x))`

`f(x+1)`

`\sqrt[3]{(x+1)+2}`

`\sqrt[3]{x+1+2}`

`\sqrt[3]{x+3}` which is the required result for
`h(x)`.