The domain of ^ - 1 [ _3 ( x 3 ) ] is - Vidyadip

MCQ

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

✓
$[1, 9]$
B
$[-1, 9]$
C
$[-9, 1]$
D
$[-9, -1]$

✓

Answer

Correct option: A.

$[1, 9]$

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

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

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

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