If $f : R \to R$ is defined by $f(x) = 2x + \cos x$,then $f$ is

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 function $f: R \to R$ defined by $f(x) = x^2$ for all $x \in R$ is

Show that the Signum Function $f: R \rightarrow R$,given by $f(x) = \begin{cases} 1, & \text{if } x > 0 \\ 0, & \text{if } x = 0 \\ -1, & \text{if } x < 0 \end{cases}$ is neither one-one nor onto.

Let $f: N \rightarrow N$ be defined by $f(n) = \begin{cases} \frac{n+1}{2}; & \text{if } n \text{ is odd} \\ \frac{n}{2}; & \text{if } n \text{ is even} \end{cases}$, for all $n \in N$ then $f$ is $\dots \dots \dots$

Let $Z$ denote the set of integers. Define $f: Z \rightarrow Z$ by $f(x) = \begin{cases} \frac{x}{2}, & x \text{ is even} \\ 0, & x \text{ is odd} \end{cases}$. Then $f$ is: