Answer
True.
Work Step by Step
This is the definition of the inverse tangent function, hence it is true. The inverse tangent function gives from the result of the tangent function the original angle.
The domain of $\tan^{-1}{x}$ is the range of $\tan{x}$, which is the real numbers.
The range of $\tan^{-1}{x}$ is a specified domain of $\tan{x}$, i.e. $\left(− \frac{\pi}{2} , \frac{\pi}{2} \right)$.
