## Precalculus (6th Edition)

$-\displaystyle \frac{\pi}{4}$
$y=\tan^{-1} x =\arctan x$ Domain: $(-\infty, \infty)$ Range: $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ ----------- $y$ is the number from $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ such that $\tan y=-1$ $\displaystyle \tan(-\frac{\pi}{4})=-1\qquad$and$\displaystyle \quad -\frac{\pi}{4}\in(-\frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ so $\tan^{-1} (-1) =-\displaystyle \frac{\pi}{4}$