Question

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

• A. $\left[0, \frac {\pi}{2}\right]$
• B. $\left[0, \frac {\pi}{2}\right] \cup \left[\frac {3 \pi}{2},2\pi \right]$
• C. $\left[\frac {3 \pi}{2},2\pi \right]$
• D. $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$

Answer 1

Answer: (B)

$\left[0, \frac {\pi}{2}\right] \cup \left[\frac {3 \pi}{2},2\pi \right]$

Answer 2

The correct answer is B:$[0,\frac{\pi}{2}]\cup[\frac{3\pi}{2},2\pi]$
Given that;
$f(x)=\sqrt{cosx}$
$\therefore$ $cosx≥0$
i.e., $x\in[2n\pi+0,2n\pi+\frac{\pi}{2}]\cup[2n\pi+\frac{3\pi}{2},2n\pi+2\pi]$
where,$n\in{z}$
For n=0
$x\in[0,\frac{\pi}{2}\cup[\frac{3\pi}{2},2\pi]$