Showing $f^{-1}$ exists where $f(x) = \frac{x+2}{x-3}$ Let $f(x) = \dfrac{x + 2 }{x - 3}$.
There's three parts to this question:


*

*Find the domain and range of the function $f$.

*Show $f^{-1}$ exists and find its domain and range.

*Find $f^{-1}(x)$.


I'm at a loss for #2, showing that the inverse function exists.  I can find the inverse by solving the equation for $x$, showing that it exists without just solving for the inverse. Can someone point me in the right direction? 

It is a valid way to find the inverse by solving for x first and then verify that $f^{-1}(f(x))=x$ for all $x$ in your domain. It is quite preferable to do it here because you need it for 3. anyways.
