WBJEE · Maths · Functions
The domain of the function \(f(x)=\sqrt{\cos ^{-1}\left(\frac{1-|x|}{2}\right)}\) is
- A \((-3,3)\)
- B \([-3,3]\)
- C \((-\infty,-3) \mathrm{U}(3, \infty)\)
- D \((-\infty,-3] \mathrm{U}[3, \infty)\)
Answer & Solution
Correct Answer
(B) \([-3,3]\)
Step-by-step Solution
Detailed explanation
Hints: \(f(x)=\sqrt{\cos ^{-1}\left(\frac{1-|x|}{2}\right)}\) \[ -1 \leq \frac{1-|\mathrm{x}|}{2} \leq 1 \Rightarrow-2-1 \leq-|\mathrm{x}| \leq 2-1 \Rightarrow-3 \leq-|\mathrm{x}| \leq 1 \Rightarrow-1 \leq \mathrm{x} \mid \leq 3 \Rightarrow \mathrm{x} \in[-3,3] \]
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