Question

Find the range of $f\left(x\right)=\frac{1}{2\left|\cos x\right|-3}$

Answer 1

$y=\frac{1}{2\left|\cos x\right|-3}\Rightarrow \cos x=\pm \frac{1+3y}{2}$
$\Rightarrow x={\cos }^{-1}(\pm \frac{1+3y}{2})$
As $-1\le \cos \theta \le 1$
$\therefore f\left(x\right)ϵ[-1,1]$