Number of integer(s) in the domain of the function $f (x) = {cos}^{- 1} (x^{2} - 4)$ is

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Solution

$f (x) = {cos}^{- 1} (x^{2} - 4)$
$∵ - 1 \leq x^{2} - 4 \leq 1$
$\Rightarrow 3 \leq x^{2} \leq 5$
$\Rightarrow x \in [- \sqrt{5}, - \sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]$

Hence, the domain of $f (x)$ is $[- \sqrt{5}, - \sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]$
There are only $2$ integers i.e., $- 2, 2$

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