If $[x]$ is the greatest integer function and $2[2x - 5] - 1 = 7$,then $x$ lies in

The set of all real values of $x$ for which the real-valued function $f(x) = \left(1 + \frac{1}{x}\right)^x$ is defined,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

The range of the function $f(x) = \frac{x^2+x+1}{x^2-x+1}$ is

Let $R-(\alpha, \beta)$ be the range of $f(x) = \frac{x+3}{(x-1)(x+2)}$. Then,the sum of the intercepts of the line $\alpha x + \beta y + 1 = 0$ on the coordinate axes is:

Let $A = \{10, 11, 12, 14, 26\}$ and let $f: A \rightarrow N$ be defined such that $f(a) = \text{highest prime factor of } a$,where $a \in A$. Then the range of $f$ is: