Let $R : \mathbb{R} \to \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers and R be a relation. An element $(x, y) \in R$ if $x + y - \sqrt{2}$ belongs to the set of irrational numbers. Then the relation R is :

The function $f: [-1, 1] \rightarrow R$ (set of real numbers) given by $f(x) = \frac{x}{x+3}$ is

Let N be set of natural numbers, then the function $f: \mathbb{N} \rightarrow \mathbb{N}$, defined by

$f(x) = \begin{cases} \frac{n+1}{2} & \text{, if } n \text{ is odd} \\ \frac{n}{2} & \text{, if } n \text{ is even} \end{cases}$, is

The number of all onto functions from the set {1, 2, .......n} to itself is

The inverse of the function $f : R \to R$ given by $f(x) = 2x + 7$ is :

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = \frac{x}{x^2+1}$ then

If $A = R - \{2\}$ and $B = R - \{1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \frac{x-1}{x-2}$, then $f$ is