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 $x$).

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

The domain of the function $f(x) = \exp (\sqrt {5x - 3 - 2{x^2}} )$ is

Let $D$ be the domain of the function $f(x) = \sin^{-1} \left(\log_{3x} \left(\frac{6+2 \log_3 x}{-5x}\right)\right)$. If the range of the function $g: D \rightarrow R$ defined by $g(x) = x - [x]$ (where $[x]$ is the greatest integer function) is $(\alpha, \beta)$,then $\alpha^2 + \frac{5}{\beta}$ is equal to

The range of $f(x) = \cos[x]$ for $-\frac{\pi}{4} < x < \frac{\pi}{4}$ (where $[.]$ represents the greatest integer function less than or equal to $x$) is

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