The function $f: C \rightarrow C$ defined by $f(x) = \frac{ax + b}{cx + d}$ for $x \in C$, where $bd \neq 0$, reduces to a constant function if:

Function $f: R \rightarrow R$ defined by $f(x) = x^3$ 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

If a function $f: Z \rightarrow Z$ is defined by $f(x) = x - (-1)^x$,then $f(x)$ is

If $f:[0, \infty) \to [0, \infty)$ and $f(x) = \frac{x}{1+x}$,then $f$ is

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