If $R = \{ (x, y) | x, y \in Z, x^2 + y^2 \le 4 \}$ is a relation in $Z$,then the domain of $R$ is:

Let $f: R - \{2, 6\} \rightarrow R$ be a real-valued function defined as $f(x) = \frac{x^2+2x+1}{x^2-8x+12}$. Then the range of $f$ is

The domain and range for the function $f(x) = e^{|x| \sin x}$ are:

If the domain of the real valued function $f(x) = \frac{1}{\sqrt{\log_{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a, b)$,then $2b =$

Range of the function $f(x) = \frac{x^2+x+2}{x^2+x+1}, x \in R$ is

The sum of all the elements in the range of $f(x) = \text{Sgn}(\sin x) + \text{Sgn}(\cos x) + \text{Sgn}(\tan x) + \text{Sgn}(\cot x)$,where $x \neq \frac{n\pi}{2}, n \in \mathbb{Z}$ and $\text{Sgn}(t) = \begin{cases} 1, & \text{if } t > 0 \\ -1, & \text{if } t < 0 \end{cases}$,is