Q. The domain of $\sin^{- 1}\left\lbrack \log_{2}\left( \frac{x}{12} \right) \right\rbrack$ is
A) [2, 12]
B) [-1, 1]
C) $\left\lbrack \frac{1}{3},\ 24 \right\rbrack$
D) [6, 24]
Explanation
(d)
For domain of given function
$\ \ \ \ \ \ \ \ - 1 \leq \log_{2}\left\{ \frac{x}{12} \right\} \leq 1$
$\Rightarrow \ \ 2^{- 1} \leq \frac{x}{12} \leq 2$
$\Rightarrow \ \ 6 \leq x \leq 24$
$\Rightarrow \ \ \ x \in \lbrack 6,\ 24\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.