Question

Find the domain of the following function:

$f\left(x\right)=\sqrt{e^{{\cos }^{-1}\left({\log }_4{x}^2\right)}}$, the domain is
$x\in [-k,-1/k]\cup [1/k,k]$
then k is?

Answer 1

$f\left(x\right)=\sqrt{e^{{\cos }^{-1}\left({\log }_4{x}^2\right)}}$ is real
when $-1\le {\log }_4{x}^2\le 1$
$\Rightarrow \frac{1}{4}\le x^2\le 4$
Therefore, $x\in [-2,-1/2]\cup [1/2,2]$