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Problem:
Find the inverse of the following function: $\sin ^{-1}\left(\frac{9}{2}-\frac{9 x}{2}\right)$
Answer:
$\left\{\left\{x\to \fbox{$\frac{1}{9} (9-2 \sin (y))\text{ if }-\frac{\pi }{2}\leq y\leq \frac{\pi }{2}$}\right\}\right\}$