Question

Find the domain of $f\left(x\right)=2{\cos }^{-1}2x+{\sin }^{-1}x$

Answer 1

$f\left(x\right)=2{\cos }^l\left(2x\right)+{\sin }^l\left(x\right)$

$2xϵ[-1,1]$ $xϵ[-1,1]$ ....(2)

$xϵ[\frac{-1}{2},\frac{1}{2}]$ ...(1)

$\therefore \left(1\right)\cap \left(2\right)$

$\Rightarrow xϵ[\frac{1}{2},\frac{1}{2}]$ Answer