The domain of y = cos - 1 ( x 2 - 4 ) is:

Question

The domain of $y = \cos^{- 1} (x^{2} - 4)$ is:

Smart Achievers · Accepted Answer

(4)

Ans. $[- \sqrt{5}, - \sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]$

Explanation:

$y = \cos^{- 1} (x^{2} - 4)$

$\Rightarrow$ $\cos y = x^{2} - 4$

i.e., $- 1 \leq x^{2} - 4 \leq 1$ (since $- 1 \leq \cos y \leq 1$ )

$\Rightarrow 3 \leq x^{2} \leq 5$

$\Rightarrow \sqrt{3} \leq | x | \leq \sqrt{5}$

$\Rightarrow x \in [- \sqrt{5}, - \sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]$

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