Textbook Problem

Give an example of mapping $f$ and $g,$ different from those in Example 3, such that one of $f$ or $g$ is not one-to-one but $f\circ g$ is one-to-one.

Example 3.

Let $A=\left\{-1,0,1\right\}$. Find mappings $f:A\to A$ and $g:A\to A$ such that $f\circ g\ne g\circ f$.