Let $A = \{x \in R : x \text{ is not a positive integer}\}$. Define a function $f : A \to R$ as $f(x) = \frac{2x}{x - 1}$. Then $f$ is

Let $A \subseteq R, B \subseteq R$ and $f: A \rightarrow B$ be defined by $f(x)=x^2-3x+2$. If $f$ is a bijection,then

Let $A = \{1, 2, 3, 4, 5, 6\}$. The number of functions $f: A \to A$ such that $f(m) + f(n) = 7$ whenever $m + n = 7$ is:

Let $A$ be the set of all $50$ students of Class $X$ in a school. Let $f: A \rightarrow N$ be a function defined by $f(x) = \text{roll number of the student } x$. Show that $f$ is one-one but not onto.

Let $A = \{x_1, x_2, \dots, x_7\}$ and $B = \{y_1, y_2, y_3\}$ be two sets containing seven and three distinct elements respectively. The total number of onto functions $f : A \to B$ such that there exist exactly three elements $x$ in $A$ with $f(x) = y_2$ is equal to:

The functions which map $[-1, 1]$ to $[0, 2]$ are