Let $f: X \rightarrow X$ be such that $f(f(x)) = x$ for all $x \in X$ and $X \subseteq \mathbb{R}$. 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

The function $f(x) = \frac{e^{|x|} - e^{-x}}{e^x + e^{-x}} + \cos^3\left(\frac{x}{2}\right)$ from $R$ to itself is

The function $f: C \rightarrow C$ defined by $f(x) = \frac{ax + b}{cx + d}$ for $x \in C$, where $bd \neq 0$, reduces to a constant function if:

Let $A = \{1, 2, 3, \ldots, 7\}$ and let $P(A)$ denote the power set of $A$. If the number of functions $f: A \rightarrow P(A)$ such that $a \in f(a)$ for all $a \in A$ is $m^n$,where $m, n \in N$ and $m$ is the least possible value,then $m + n$ is equal to . . . . . . .

$f:[-2,2] \rightarrow[-2,2]$ and $g:[-2,2] \rightarrow[0,4]$ are two functions defined as $f(x)=\begin{cases} -2, & -2 \leq x \leq 0 \\ x^2-2, & 0 \leq x \leq 2 \end{cases}$ and $g(x)=|f(x)|+f(|x|)$, then