# $f:N\rightarrow Z$ is a function defined as $f(n)=\left\{ \begin {array} {1 1} \large\frac{n-1}{2}, \:\:when\:\: n\:\: is\:\: odd \\ -\large \frac{n}{2},\:\:when\:\: n\:\: is\:\: even \\ \end{array} \right.$, then $f$ is

$\begin{array}{1 1} neither\;1-1\;nor\;onto \\ many \;to\;one\;onto \\ 1-1 \;but\;not\;onto \\ both \;1-1\;and\;onto \end{array}$

$f(1)=0$
$f(2)=-1$
$f(3)=1$
$f(4)=-2$ ........
Each natural number is related with only one integer
$\Rightarrow$ $f$ is 1-1 and onto.
answered May 13, 2013
edited May 17, 2014