Domain of $f(x) = \frac{x}{1-|x|}$ is

Let $f:[2, \infty) \rightarrow R$ be the function defined by $f(x)=x^{2}-4x+5$. Then the range of $f$ is:

If the domain of the function $f(x) = \sqrt{\ln(m\sin x + 4)}$ is $R$,then the number of possible integral values of $m$ is:

If $f: R \rightarrow A$,defined by $f(x) = \cos x + \sqrt{3} \sin x - 1$,is an onto function,then $A =$

The range of $f(x) = \sec \left( \frac{\pi }{4} \cos^2 x \right)$ for $-\infty < x < \infty$ 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 $(f/g)(x) = \frac{f(x)}{g(x)}$?