Question

The domain of the function $f\left(x\right) = \sqrt{\cos^{-1}\left(\frac{1-\left|x\right|}{2}\right)}$ 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 $+1$ ]
$-1 \leq \frac{1-|x|}{2} \leq 1$
$\Rightarrow -2-1 \leq-|x| \leq 2-1$
$\Rightarrow -3 \leq-|x| \leq 1$
$\Rightarrow -1 \leq|x| \leq 3$
$\Rightarrow x \in[-3,3]$