Finding and verifying an inverse $[5\mathrm{.}2]$

$2.$ On a test you will be asked to find the inverse and then verify your result. To verify your result you must show $(f{f}^{-1})(x)=x$ and $(f^{-1}$@$f)(x)=x.$ Find the inverse of $f(x)$ and then verify your result.

$f(x)=\frac{1}{x-3}$