Properties of Inverse Functions

A necessary condition for a function to have an inverse is that it is one-to-one.

For a function to have an inverse, it must be periodic.

The graph of an inverse function is the reflection of the original function across the line $y=x$.

If $f$ is invertible, then $f^{-1}(f(x))=x$ for every $x$ in the domain of $f$.