If a set $A$ has $n$ elements,then the number of functions defined from $A$ to $A$ that are not one-one is

$A$ function $f$ from the set of natural numbers $\mathbb{N}$ to the set of integers $\mathbb{Z}$ is defined by $f(n) = \begin{cases} \frac{n-1}{2}, & \text{if } n \text{ is odd} \\ -\frac{n}{2}, & \text{if } n \text{ is even} \end{cases}$. The function $f$ is:

Given that $f: S \rightarrow R$ is said to have a fixed point at $c \in S$ if $f(c)=c$. Let $f:[1, \infty) \rightarrow R$ be defined by $f(x)=1+\sqrt{x}$. Then:

Let $A = \{x, y, z, u\}$ and $B = \{a, b\}$. $A$ function $f: A \rightarrow B$ is selected randomly. The probability that the function is an onto function is

Let a function $f: (0, \infty) \to (0, \infty)$ be defined by $f(x) = |1 - \frac{1}{x}|$. Then $f$ is

The function $f(x) = \sin (\log (x + \sqrt {x^2 + 1}))$ is