Inverse Functions

You feed 5 into a machine and it outputs 25. What button would you press to get 5 back? You'd want a second machine that takes 25 and returns 5 — the UNDO of the first. That's an inverse function, written f⁻¹. If f turns inputs into outputs, f⁻¹ turns those outputs back into the inputs that made them. But there's a catch: not every function can be undone unambiguously, and discovering why is the heart of this lesson.