Question

The domain of ${\sin }^{-1}[{\log }_3(x/3)]$ is

• A. [1, 9]
• B. [-1, 9]
• C. [-9, 1]
• D. [-9, -1]

Answer 1

Answer: (A)

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