## 1.4 Inverse Functions

#### Inverse Functions

- A function maps the domain to the range. An inverse function simply does the opposite.

- However, recall that a function must have the type of relation which is a one-to-one relation. Therefore, if the inverse function (which, yes, is a function) exists, the inverse must have a one-to-one relation too.

- This implies that for an inverse function to exist (might be over a certain subset of the domain), the function must be one-to-one (over that particular subset if applicable).

- We denote the inverse of f as f^{-1}. In particular, if f(x)=y, then f^{-1}(y)=x.

- Therefore, we can deduce that: