Q. If $n$ is an integer, the domain of the function $\sqrt{\sin{2x}}$ is
A) $\left\lbrack n\pi - \frac{\pi}{2},\ n\pi \right\rbrack$
B) $\left\lbrack n\pi,\ n\pi + \frac{\pi}{4} \right\rbrack$
C) $\lbrack(2n - 1)\pi,\ 2n\pi\rbrack$
D) $\lbrack 2n\pi,\ (2n + 1)\pi\rbrack$
Explanation
(b)
Let $y = \sqrt{\sin{2x}} \Rightarrow 0 \leq \sin{2x \leq 1}$,
$\Rightarrow \ \ \ 0 \leq 2x \leq \frac{\pi}{2}$
$\Rightarrow \ \ \ 0 \leq x \leq \frac{\pi}{4}$
$\Rightarrow \ \ x \in \left\lbrack n\pi,\ n\pi + \frac{\pi}{4} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.