Question

Find the domain of ${\cos }^{-1}\frac{\pi -x}{\pi }$

Answer 1

Domain of $f\left(x\right)={\cos }^{-1}\left(x\right)$ is $[-1,1]$

$⟹-1\le \frac{\pi -x}{\pi }\le 1-\pi \le \pi -x\le \pi -2\pi \le -x\le 00\le x\le 2\pi$

So domain of $f\left(x\right)$ is $[0,2\pi ]$