Let [•] denote the greatest integer function. If the domain of the function

$f(x)=\cos ^{-1}\left(\frac{4 x+2[x]}{3}\right)$ is $[\alpha, \beta]$, then $12(\alpha+\beta)$ is equal to :

The number of functions $f:\{1,2,3,4\} \rightarrow\{a, b, c\}$, which are not onto, is :

Given below are two statements :

Statement I : The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \frac{x}{1 + |x|}$ is one-one.

Statement II : The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \frac{x^2 + 4x - 30}{x^2 - 8x + 18}$ is many-one.

In the light of the above statements, choose the correct answer from the options given below :

The sum of all the elements in the range of $f(x) = \text{Sgn}(\sin x) + \text{Sgn}(\cos x) + \text{Sgn}(\tan x) + \text{Sgn}(\cot x)$, $x \neq \frac{n\pi}{2}, n \in \mathbb{Z}$, where

$\text{Sgn}(t) = \begin{cases} 1, & \text{if } t > 0 \\ -1, & \text{if } t < 0 \end{cases}$

is :