The domain of the function $f(x) = \sqrt{cosx}$ is

The correct answer is $\left [ 0, \dfrac{\pi}{2} \right ]$ $\cup \left [ \dfrac{3\pi}{2}, 2\pi \right ]$

We know that square root is defined only for non-negative number.

Hence for $f(x) = \sqrt{cosx}$ to be defined

⇒ $cos x > 0$

⇒ $x$ should lie in 1st or 4th quadrant including ends of the quadrant.

⇒ $x \in \left [ 2n \pi + 0, 2n \pi + \dfrac{\pi}{2} \right ]$ $\cup \left [ 2n \pi + \dfrac{3\pi}{2}, 2n \pi + 2\pi \right ]$

where $n \in Z$, for $n = 0$