Question

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

Answer 1

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

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