#### Answer

$-\displaystyle \frac{\pi}{4}$

#### Work Step by Step

$y=\tan^{-1} x =\arctan x$
Domain: $(-\infty, \infty) $
Range: $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$
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$y$ 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
$\tan^{-1} (-1) =-\displaystyle \frac{\pi}{4}$