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

If $f: R \rightarrow R$ is defined by $f(x) = [\frac{x}{5}]$ for $x \in R$, where $[y]$ denotes the greatest integer not exceeding $y$, then $\{f(x) : |x| < 71\}$ is equal to

Find the domain of the real-valued function $f(x) = ([x]^2 - [x] - 2)^{-1/2}$,where $[\cdot]$ denotes the greatest integer function.

Find the domain of the function $f(x) = \frac{x^{2}+2x+1}{x^{2}-8x+12}$.

If the domain of the function $f(x) = \cos^{-1}\left(\frac{2-|x|}{4}\right) + (\log_e(3-x))^{-1}$ is $[-\alpha, \beta) \setminus \{\gamma\}$,then $\alpha + \beta + \gamma$ is equal to:

The function $f: R \rightarrow R$ is defined by $f(x) = \cos^2 x + \sin^4 x$ for $x \in R$. Then $f(R)$ is equal to: