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

Let $f : R \to R$ be defined by $f(x) = \frac{x}{1 + x^2}, x \in R$. Then the range of $f$ is

Let $[x]$ denote the greatest integer $\leq x$,where $x \in \mathbb{R}$. If the domain of the real-valued function $f(x) = \sqrt{\frac{|[x]|-2}{|[x]|-3}}$ is $(-\infty, a) \cup [b, c) \cup [4, \infty)$,where $a < b < c$,then the value of $a+b+c$ is:

The domain of the function $f(x) = \sin^{-1}[2x^2 - 3] + \log_2(\log_{1/2}(x^2 - 5x + 5))$,where $[t]$ is the greatest integer function,is:

If the range of the function $f(x) = -3x - 3$ is $\{3, -6, -9, -18\}$, then which of the following elements is not in the domain of $f$?

Domain of the function $f(x) = \frac{x^2 - 3x + 2}{x^2 + x - 6}$ is