A one-to-one function maps distinct domain inputs to distinct range outputs. Injectivity is the necessary and sufficient condition for a function to possess an inverse function.
Quick Reference
| Term / Test | Condition | Meaning |
|---|---|---|
| One-to-One (Injective) | No two inputs share the same output | |
| Horizontal Line Test | Intersects graph at most once | Geometric test for injectivity |
Definition of One-to-One
A function is called one-to-one (or injective) if it never takes on the same value twice; that is:
Equivalently:
Horizontal Line Test
Horizontal Line Test: A function is one-to-one if and only if no horizontal line intersects its graph more than once.
