Q. The domain of the function $\sin^{-}\left( \log_{2}\frac{x^{2}}{2} \right)$ is
A) [-1, 2]-{0}
B) [-2, 2]-(-1, 1)
C) [-2, 2]-{0}
D) [1, 2]
Explanation
(b)
Foe domain of given function
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ - 1 \leq \log_{2}{\frac{x^{2}}{2} \leq 1}$
$\Rightarrow \ \ \ 2^{- 1} \leq \frac{x^{2}}{2} \leq 2\ \Rightarrow 1 \leq x^{2} \leq 4$
$\Rightarrow \ \ \ \ |x| \leq 2$ and $|x| \geq 1$
$\Rightarrow \ \ \ \ \ \ \ x \in \lbrack - 2,\ 2\rbrack - ( - 1,\ 1)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.