If set $A$ has $5$ elements and set $B$ has $7$ elements,then the number of many-one functions that can be defined from $A$ to $B$ is:

If the function $f:[-1,1] \rightarrow R$ is defined by $f(x) = \begin{cases} 2^x+1, & \text{for } x \in [-1,0) \\ 1, & \text{for } x=0 \\ 2^x-1, & \text{for } x \in (0,1] \end{cases}$,then in $[-1,1]$,$f(x)$ has

Let $A$ be a set containing $10$ distinct elements. Then the total number of distinct functions from $A$ to $A$ is:

If a function $f: Z \rightarrow Z$ is defined by $f(x) = x - (-1)^x$,then $f(x)$ is

Show that a one-one function $f: \{1, 2, 3\} \rightarrow \{1, 2, 3\}$ must be onto.

Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x + 2, & x \leq -1 \\ x^2, & -1 < x < 1 \\ 2 - x, & x \geq 1 \end{cases}$. Then the value of $f(-1.75) + f(0.5) + f(1.5)$ is