Question

If f(g(x)) = g(f(x)) = x, and
g(x) = 2 + In(x + 1), find f(4).

Answer 1

If
`f(g(x))=g(f(x))=x`, then
`g` and
`f` are inverses of one another. So we know
`g(f(4))=4`.

`g(f(4))=2+\ln(f(4)+1)=4`

`\implies\ln(f(4)+1)=2`

`\implies f(4)+1=e^2`

`\implies\boxed{f(4)=e^2-1}`