If a function $f: R-\{l\} \to R-\{m\}$ defined by $f(x) = \frac{x+3}{x-2}$ is a bijection,then $3l - 2m =$

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

If $f: R \rightarrow R$ is defined as $f(x)=x^2-2x-3$,then $f$ 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.

If $P(S)$ denotes the set of all subsets of a given set $S$,then the number of one-to-one functions from the set $S = \{ 1, 2, 3 \}$ to the set $P(S)$ is

Let $f, g: N - \{1\} \rightarrow N$ be functions defined by $f(a) = \alpha$,where $\alpha$ is the maximum of the powers of those primes $p$ such that $p^{\alpha}$ divides $a$,and $g(a) = a + 1$,for all $a \in N - \{1\}$. Then,the function $f + g$ is.