Q. The domain of $\sin^{- 1}{(\log_{3}x)}$ is
A) [-1, 1]
B) [0, 1]
C) $\lbrack 0,\ \infty\rbrack$
D) $\left\lbrack \frac{1}{3},\ 3 \right\rbrack$
Explanation
(d)
For domain of $\sin^{- 1}{(\log_{3}x)}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - 1 \leq \log_{3}{x \leq 1}\$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3^{- 1} \leq x \leq 3$
$\therefore$ Domain of $\sin^{- 1}{(\log_{3}x)}$ is $\left\lbrack \frac{1}{3},\ 3 \right\rbrack$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.