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

Let $f:(1,3) \rightarrow R$ be a function defined by $f(x)=\frac{x[x]}{1+x^{2}},$ where $[x]$ denotes the greatest integer $\leq x.$ Then the range of $f$ is

The domain of the definition of the function $f(x) = \sqrt{\frac{4 - x^2}{[x] + 2}}$ is (where $[.] \rightarrow \text{G.I.F.}$)

The range of the function $f(x) = (\sin x)^{\sin x}$ defined on $(0, \pi)$ is

Domain of the real valued function $f(x) = \log(x^2 - 1) + x \operatorname{coth}^{-1} x$ is

The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - 3[x] - 10}}$ is (where $[x]$ denotes the greatest integer less than or equal to $x$).