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

If ${ }^{n} C_{r}$ denotes the number of combinations of $n$ distinct things taken $r$ at a time, then the domain of the function $g(x)={ }^{(16-x)} C_{(2 x-1)}$ is

Domain of $f(x) = \frac{x}{1-|x|}$ is

Given that $a, b$ and $c$ are real numbers such that $b^2 = 4ac$ and $a > 0$. The maximal possible set $D \subseteq R$ on which the function $f: D \rightarrow R$ given by $f(x) = \log \{ax^3 + (a+b)x^2 + (b+c)x + c\}$ is defined,is

The domain of the function $f(x) = \frac{1}{\sqrt{|x|-x}}$ is

Find the domain and the range of the real function $f$ defined by $f(x) = \sqrt{x-1}$.