A function $h(Y)$ is called invertible, if there is a one-to-one correspondence between the input $y$ and the output $h(y)$. This means:
- *Forward direction:* Knowing $y$ uniquely determines $h(y)$.
- *Backward direction:* Knowing $h(y)$ uniquely determines $y$.
Mathematically invertibility is defined as:
$ h(y_1)=h(y_2) \implies y_1=y_2$
**Counter example:** For $h(y)=y^2$ we can different inputs, e.g. $(y=2)$ or $(y=-2)$ that yield that same output. Thus, the function is not invertible.