Q. The domain of the function $f(x) = \sqrt{\cos^{- 1}\left( \frac{1 - |x|}{2} \right)}$ is
A) (-3, 3)
B) [-3, 3]
C) $( - \infty,\ - 3) \cup (3,\ \infty)$
D) $( - \infty,\ - 3\rbrack \cup \lbrack 3,\ \infty)$
Explanation
(b)
$f(x) = \sqrt{\cos^{- 1}\left( \frac{1 - |x|}{2} \right)}$
$\ \ \ \ - 1 \leq \frac{1 - |x|}{2} \leq 1 \Rightarrow - 2 - 1 \leq - |x| \leq 2 - 1$
$\Rightarrow \ - 3 \leq - |x| \leq 1 \Rightarrow - 1 \leq |x| \leq 3 \Rightarrow x \in \lbrack - 3,\ 3\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.