Answer
$(-\frac{\pi}{2}, \frac{\pi}{2})$, $tan^{-1}(x)$.
Work Step by Step
To have an inverse, a function needs to pass the horizontal line test. For $y=tan(x)$, we need to restrict the domain so that an inverse can be found, and the restricted domain is $(-\frac{\pi}{2}, \frac{\pi}{2})$. We use a special symbol $f^{-1}$ to denote an inverse, and the inverse of $y=tan(x)$ is $y=tan^{-1}(x)$.
