Question

if $f\left(x\right)=\pi \left(\frac{\sqrt{x+7}-4}{x-9}\right)$, then the range of function $y=\sin \left(2f\right(x\left)\right)$ is :

Answer 1

$f\left(x\right)=\pi \left(\frac{\sqrt{x+7}-4}{x-9}\right)$

$y=\sin \left(2f\right(x\left)\right)$

$=\sin \left(2\pi \left(\frac{\sqrt{x+7}-4}{x-9}\right)\right)$

Find the range

$-1\le \sin \left(2\pi \frac{\sqrt{x-7}-4}{x-9}\right)\le 1$