The function $f:R \to R$ defined by $f(x) = e^x$ is

Let $A$ and $B$ be sets. Show that $f: A \times B \rightarrow B \times A$ defined by $f(a, b) = (b, a)$ is a bijective function.

Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements,and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then ...... .

Let $f : X \rightarrow Y$ be a function such that $f(x) = \sqrt{x - 2} + \sqrt{4 - x} .$ Then the set of $X$ and $Y$ for which $f(x)$ is both injective as well as surjective,is-

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

Let $f: N \rightarrow N$ be defined by $f(n) = \begin{cases} \frac{n+1}{2}; & \text{if } n \text{ is odd} \\ \frac{n}{2}; & \text{if } n \text{ is even} \end{cases}$. Then $f$ is: