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

MCQ

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

A
$[-1, 1]$
B
$[0, 1]$
C
$[0, \infty $]
✓
$ \left[ {\frac{1}{3},\,3} \right]$

✓

Answer

Correct option: D.

$ \left[ {\frac{1}{3},\,3} \right]$

d
(d) $ - 1 \le {\log _3}x \le 1$; ${3^{ - 1}} \le x \le 3$

==> $\frac{1}{3} \le x \le 3$

$\therefore$ Domain of function $ = \left[ {\frac{1}{3},\,3} \right]$.

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