The domain of function f(x)=(√(4-x^2))/(sin^-1|x|) is

$f(x)=\frac{\sqrt{4-x^2}}{\sin^{-1}|x|}$

$⇒4-x^2≥0$

So $x^2≤4$

so $-2≤x≤2⇒x∈[-2,2]$

so $\sin^{-1}|x|⇒1≥|x|≥0=-1≤x≤1-\{0\}$

$x∈[-1,1]-\{0\}$

So $x∈[-1, 0) ∪ (0, 1]$