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  4. The domain of sin-1 [ log3 (x/3) ] is

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Q. The domain of $\sin^{-1} [\log_3 (x/3) ]$ is

Relations and Functions - Part 2

Solution:

$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) \le1 \Leftrightarrow 3^{-1} \le\frac{x}{3} \le 3^{1} $
$\Leftrightarrow 1 \le x \le 9$ or $x \in\left[1,9\right] $