If $f: R \to R$,then the range of the function $f(x) = \frac{x^2}{x^2 + 1}$ is

The domain of definition of $f(x) = \sqrt{\frac{1-|x|}{2-|x|}}$ is: (Here $(a, b) = \{x : a < x < b\}$ and $[a, b] = \{x : a \leq x \leq b\}$)

If the domain of the function $f(x) = \frac{[x]}{1+x^2}$,where $[x]$ is the greatest integer $\leq x$,is $(2, 6)$,then its range is

If $f: R \rightarrow R$ is defined by $f(x) = \frac{1}{2 - \cos 3x}$ for each $x \in R$,then the range of $f$ is

The domain of the function $f(x) = \sqrt{\log_{10}\left(\frac{5x - x^2}{4}\right)}$ is:

The real-valued function $f(x) = \frac{\operatorname{cosec}^{-1} x}{\sqrt{x - [x]}}$,where $[x]$ denotes the greatest integer less than or equal to $x$,is defined for all $x$ belonging to: