Let $f(x)=2+\ln (2-x)^2$ and $g(x)=2+3 \mathrm{e}^x$.
(a) Starting with the graph of $y=\ln x$, sketch the graph of $f(x)$ and its inverse if it exists.
(b) Show $g(x)$ is one to one. Find $g^{-1}(5)$ if it exists.