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

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 $(f/g)(x) = \frac{f(x)}{g(x)}$?

The domain and range of $f(x) = \frac{|x - 3|}{x - 3}$ are respectively:

Find the domain and the range of the real function $f$ defined by $f(x) = \sqrt{x-1}$.

Range of the function $f(x) = \frac{x^2}{x^2 + 1}$ is

The range of the function $f(x) = x^2 + \frac{1}{x^2+1}$ is