Show that the Signum Function `f : R->R ,`given by `f(x)={[1 if x>0], [0 if x=0],[-1 if x< 0]}`is neither one-one nor onto.

Explanation

To show that the Signum Function \( f : \mathbb{R} \to \mathbb{R} \) defined by

\[
f(x) =
\begin{cases}
1 & \text{if } x > 0 \\
0 & \text{if } x = 0 \\
-1 & \text{if } x < 0
...