The domain of the real-valued function $f(x) = \sqrt[3]{\frac{x-2}{2x^2-7x+5}} + \log(x^2-x-2)$ is

The sum of the least positive integer and the greatest negative integer in the range of the function $f(x) = \frac{x^2-5x+7}{x^2-5x-7}$ 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

If the range of the real valued function $f(x) = \frac{x^2+x+k}{x^2-x+k}$ is $\left[\frac{1}{3}, 3\right]$,then $k=$

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then the range of $f$ is:

The domain of $f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)$ is