Question

Domain of ${cos}^{-1}[2x^2-3]$ where $[.]$ denotes greatest integer function, is

Answer 1

${\cos }^{-1}[2x^2-3]$

We know that for ${\cos }^{-1}x$ x lies in the range of $[-1,1]$

$-1\le 2x^2-3\le 1$

$2\le 2x^2\le 4$

$1\le x^2\le 2$

$x^2-1\ge 0;x^2-2\le 0$

(Image )

$\therefore xϵ[-\sqrt{2},-1]\bigcup [1,\sqrt{2}]$