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 $g(f(4))=4$.

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

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

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

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