For $A = \{-1, -2, 3, 4\}$,the number of one-one functions from $A$ to $A$ is . . . . . . .

The function $f: R-\{1\} \rightarrow R-\{4\}$ defined by $f(x) = \frac{4x-3}{x-1}$ for $x \in R-\{1\}$ 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.

If a set $A$ has $m$ elements and the set $B$ has $n$ elements,then the number of injections from $A$ to $B$ is

Let $f: N \to N$ be defined by $f(x) = x^2 + x + 1$,where $x \in N$. Then $f$ is:

The function $f: N \rightarrow Z$ defined by $f(n) = \begin{cases} \frac{n}{2} & , n \text{ is even} \\ -\left(\frac{n-1}{2}\right) & , n \text{ is odd} \end{cases}$ is . . . . . . .