If $f: R \rightarrow R$ is defined by $f(x) = x + 2|x + 1| + 2|x - 1|$, then the element in the co-domain, which has a unique pre-image in the domain is

$f:[-2,2] \rightarrow[-2,2]$ and $g:[-2,2] \rightarrow[0,4]$ are two functions defined as $f(x)=\begin{cases} -2, & -2 \leq x \leq 0 \\ x^2-2, & 0 \leq x \leq 2 \end{cases}$ and $g(x)=|f(x)|+f(|x|)$, then

For the greatest integer function $f(x) = [x]$,where $x \in R$,which of the following is true?

If $f : R \rightarrow R$ is defined as $f(x) = x - [x] + 3$,$\forall x \in R$,then $f$ is

If $f(x)=|x-1|+|x-2|+|x-3|$ for $2 < x < 3$,then $f$ is

Let $f: R \to R$ be defined as $f(x) = x^3$. Then $f$ is . . . . . . .