The domain of the real valued function

$$ f(x)=\frac{\sqrt{\log _{10}\left(\frac{x}{x-2}\right)}}{\sqrt{[x]^2-5[x]+6}} \text { is } $$

(Here, $[x]$ denotes the greatest integer function)

The range of the real valued function $f(x)=\frac{1}{x-|x|}$ is

If $\frac{6 x^4+13 x^3+2 x^2-x+3}{2 x^2+3 x-2}=f(x)+\frac{A}{a x-1}+\frac{B}{x+b}$, then $f(\mathrm{l})+a \cdot B+b \cdot A=$

The domain of the function $f(x)=\sin ^{-1}\left(\log _2\left(\frac{x^2}{2}\right)\right)$ is