Question

Show that the Signum Function $f:R\to R$, is neither one one nor onto?

Answer 1

To show that it's not one-one, just showing a counter-example would work:
$f\left(1\right)=f\left(2\right)=1$
To show it's not onto, it can be seen that there is no $x$, such that $f\left(x\right)=2$.
Therefore, the given function is neither one-one nor onto.