If $f: R \rightarrow C$ is defined by $f(x)=e^{2 i x}$ for $x \in R$,then $f$ is (where $C$ denotes the set of all complex numbers)

For each $n \in N$,let $A_n = \{(n+1)k \mid k \in N\}$ and $X = \bigcup_{n \in N} A_n$. $A$ mapping $f: X \rightarrow N$ defined by $f(x) = x, \forall x \in X$,is

The number of bijective functions $f: Z \rightarrow Z$ such that $f(x+y)=f(x)+f(y)$ for all $x, y \in Z$ is:

Given that for any $n \in N$,there exist an odd integer $q$ and a non-negative integer $r$ such that $n$ can be written uniquely as $n = q \times 2^r$. Let $f: N \rightarrow N \times N$ be a function defined by $f(n) = \left(r+1, \frac{q+1}{2}\right)$. Then,

If $f: Z \rightarrow Z$ is defined by $f(x)=\begin{cases} \frac{x}{2}, & \text{if } x \text{ is even} \\ 0, & \text{if } x \text{ is odd} \end{cases}$,then $f$ is

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