Q100 / 160 · WBJEE 2010 · Mathematics

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

  • A
    $(-3,3)$
  • Correct answer
    B
    $[-3,3]$
  • C
    $(-\infty,-3) \mathrm{U}(3, \infty)$
  • D
    $(-\infty,-3] \mathrm{U}[3, \infty)$

Solution

Hints: $f(x)=\sqrt{\cos ^{-1}\left(\frac{1-|x|}{2}\right)}$ $$ -1 \leq \frac{1-|\mathrm{x}|}{2} \leq 1 \Rightarrow-2-1 \leq-|\mathrm{x}| \leq 2-1 \Rightarrow-3 \leq-|\mathrm{x}| \leq 1 \Rightarrow-1 \leq \mathrm{x} \mid \leq 3 \Rightarrow \mathrm{x} \in[-3,3] $$

Hence, the correct answer is option: 'B'.

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