The domain of the function f(x)=√(3-2^x-2^1-x)+√(sin^-1x) is

$\sin^{-1}x≥0⇒0≤x≤1⇒3-y-\frac{2}{y}≥0,\,2^x>0$

and $y2-3y+2≤0$ or $(y-1)(y-2)≤0$

$∴1≤x^2≤2$ or $2^0≤y≤2^1$ or $2^0≤2^x≤2^1⇒0≤x≤1$

$∴x∈[0, 1]$