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

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$[1, 9]$

$[- 1, 9]$

$[- 9, 1]$

$[- 9, - 1]$

answer is A.

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Detailed Solution

$f (x) = \sin^{- 1} (\log_{3} (\frac{x}{3}))$ exists $\Rightarrow - 1 \leq \log_{3} (\frac{x}{3}) \leq 1 \Rightarrow 3^{- 1} \leq \frac{x}{3} \leq 3^{1} \Rightarrow 1 \leq x \leq 9$

$\Rightarrow$ Domain = $[1, 9]$

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