Question

The domain of the function $f\left(x\right)=\sqrt{{\cos }^{-1}\left(\frac{1-|x|}{2}\right)}$ is

• A. $(-3,3)$
• B. $[-3,3]$
• C. $\left(-\infty ,-3\right)U\left(3,\infty \right)$
• D. $\left(-\infty ,-3\right]U\left[3,\infty \right)$

Answer 1

Answer: (B)

$f(x)=\sqrt{{\cos }^{-1}\left(\frac{1-|x|}{2}\right)}$
$[\because$ The value of cos lies between $-1$ to $+1$ ]
$-1\le \frac{1-|x|}{2}\le 1$
$\Rightarrow -2-1\le -|x|\le 2-1$
$\Rightarrow -3\le -|x|\le 1$
$\Rightarrow -1\le |x|\le 3$
$\Rightarrow x\in [-3,3]$