If n is an integer,the domain of the function | vedclass

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(B) For the function $f(x) = \sqrt{\sin 2x}$ to be defined,the expression inside the square root must be non-negative.Therefore,$\sin 2x \ge 0$.We kno

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$[n\pi, n\pi + \frac{\pi}{2}]$

Vedclass · Answer

(B) For the function $f(x) = \sqrt{\sin 2x}$ to be defined,the expression inside the square root must be non-negative.Therefore,$\sin 2x \ge 0$.We know that $\sin 	heta \ge 0$ when $	heta$ lies in the first or second quadrant,i.e.,$2n\pi \le 	heta \le 2n\pi + \pi$.Substituting $	heta = 2x$,we get $2n\pi \le 2x \le 2n\pi + \pi$.Dividing the entire inequality by $2$,we get $n\pi \le x \le n\pi + \frac{\pi}{2}$.Thus,the domain is $[n\pi, n\pi + \frac{\pi}{2}]$.Hence,option $(b)$ is correct.

If $n$ is an integer,the domain of the function $\sqrt{\sin 2x}$ is

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