Precalculus (6th Edition)

$\arcsin(-\sqrt{2})$ does not exist
$y=\sin^{-1}x =\arcsin x$ Domain: $[-1, 1]$ Range: $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ ----------- $y$ is the number from $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ such that $\sin y=-\sqrt{2}.$ Such a y can not exist, as $-1 \leq \sin y \leq 1$ ($-\sqrt{2}$ is not in the range of $\sin x,$ $-\sqrt{2}$ is not in the domain of $\sin^{-1}x$) so $\arcsin(-\sqrt{2})$ does not exist