Question

Domain of the function $f\left(x\right)=\frac{1}{x}+2^{({\sin }^{-1}x+{\cos }^{-1}x)}+\frac{1}{\sqrt{4-x^2}}$ is

Answer 1

$f\left(x\right)=\frac{1}{x}+2^{({\sin }^{-1}x+{\cos }^{-1}x)}+\frac{1}{\sqrt{4-x^2}}$

Since ${\sin }^{-1}x$ & ${\cos }^{-1}x$ is intrduced $xϵ[-1,1]$

Also, $4-x^2\ge 0$ but $x\ne 0$

$(2+x)(2-x)\ge 0$

$(x+2)(x-2)\le 0$

$xϵ[-2,2]\sim \left[0\right]$

$\therefore$ domain $\Rightarrow xϵ[-1,0)\cup (0,1]$