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), (C), (D)

Given, $f(x)=\sqrt{\cos x}$
i.e., $\cos x \geq 0$
But $-1 \leq \cos x \leq 1$
$\therefore 0 \leq \cos x \leq 1$
i.e., $x$ lies in Ist or IVth quadrant
$\Rightarrow 0 \leq x \leq \frac{\pi}{2}$ or $\frac{3 \pi}{2} \leq x \leq 2 \pi$
$\therefore x \in\left[0, \frac{\pi}{2}\right] \cup\left[\frac{3 \pi}{2}, 2 \pi\right]$
Also, $\cos (-x)=\cos x$
Hence, $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is also the domain of the function.