Q. Domain of the function $f(x) = \sin^{- 1}{(\log_{2}x)}$ in the set of real numbers is
A) $\{ x:1 \leq x \leq 2\}$
B) $\{ x:1 \leq x \leq 3\}$
C) $\{ x: - 1 \leq x \leq 2\}$
D) $\left\{ x:\frac{1}{2} \leq x \leq 2 \right\}$
Explanation
(d)
For $f(x)$ to be defined
$- 1 \leq \log_{2}{x \leq 1}$ $\lbrack\because\ - 1 \leq \sin^{- 1}{x \leq 1}\rbrack$
$\Rightarrow \ \ \ \ \frac{1}{2} \leq x \leq 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.