Domain of the function $f(x) = \frac{x^2 - 3x + 2}{x^2 + x - 6}$ is

The domain of the function $f(x) = \sqrt{\log \frac{1}{|\sin x|}}$ is

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,then the range of $f$ is (Here $[x]$ denotes the greatest integer not exceeding $x$)

The domain and range for the function $f(x) = e^{|x| \sin x}$ are:

The domain of the real-valued function $f(x) = \frac{\sqrt{\log_{10}\left(\frac{x}{x-2}\right)}}{\sqrt{[x]^2-5[x]+6}}$ is (where $[x]$ denotes the greatest integer function):

If the functions are defined as $f(x) = \sqrt{x}$ and $g(x) = \sqrt{1-x}$,then what is the common domain of the following functions: $f+g, f-g, f/g, g/f, g-f$ where $(f \pm g)(x) = f(x) \pm g(x)$ and $(f/g)(x) = \frac{f(x)}{g(x)}$?