The function $f(x) = \frac{e^{2x} - 1}{e^{2x} + 1}$ is

The number of bijective functions $f: Z \rightarrow Z$ such that $f(x+y)=f(x)+f(y)$ for all $x, y \in Z$ is:

Let $R = \{ a, b, c, d, e \}$ and $S = \{1, 2, 3, 4\}$. The total number of onto functions $f: R \rightarrow S$ such that $f(a) \neq 1$ 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

Let $X$ and $Y$ be subsets of $R$,the set of all real numbers. The function $f:X \to Y$ defined by $f(x) = x^2$ for $x \in X$ is one-one but not onto if (Here $R^+$ is the set of all positive real numbers):

Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injections that can be defined from $A$ to $B$ is