Domain of {sin ^{ - 1}}left[ {{{log }₃}left( {frac{x}{3}} right)} right] is

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1.Relation and Function

medium

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

A

$[1, 9]$

B

$[-1, 9]$

C

$[-9, 1]$

D

$[-9, -1]$

(AIEEE-2002)

Solution

(a) $y = {\sin ^{ – 1}}\left[ {{{\log }_3}\left( {\frac{x}{3}} \right)} \right]$

==> $ – 1 \le {\log _3}\left( {\frac{x}{3}} \right) \le 1$

==> $\frac{1}{3} \le \frac{x}{3} \le 3$ ==> $1 \le x \le 9$ ==> $x \in [1,\,9]$.

Standard 12

Mathematics

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