Q. The domain of $\sin^{- 1}\left\lbrack \log_{3}\left( \frac{x}{3} \right) \right\rbrack$ is
A) [1, 9]
B) [-1, 9]
C) [-9, 1]
D) [-9, -1]
Explanation
(a)
Let $y = \sin^{- 1}\left\lbrack \log_{3}\left( \frac{x}{3} \right) \right\rbrack$
$\Rightarrow \ \ - 1 \leq \log_{3}{\left( \frac{x}{3} \right) \leq 1}$
$\Rightarrow \ \ \ \ \ \frac{1}{3} \leq \frac{x}{3} \leq 3$
$\Rightarrow \ \ \ \ \ 1 \leq x \leq 9$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.