Mathematics - Functions Question with Solution | TestHub

$f(x)={\sin }^{-1}\left({\log }_3\left(\frac{x}{3}\right)\right)$ exists if $-1\le {\log }_3\left(\frac{x}{3}\right)\le 1\iff 3^{-1}\le \frac{x}{3}\le 3^1\iff 1\le x\le 9$ or $x\in [1,9]$