What is what does it mean for a function to be one to one?

A function is said to be one-to-one (also called injective) if it maps distinct elements of its domain to distinct elements of its range. In simpler terms, no two different inputs produce the same output.

Formally, a function f from a set A to a set B is one-to-one if for all a and b in A:

if f(a) = f(b), then a = b.

Equivalently, if a ≠ b, then f(a) ≠ f(b).

To determine if a function is one-to-one, you can use the Horizontal Line Test. If any horizontal line intersects the graph of the function at more than one point, then the function is not one-to-one.

Understanding one-to-one functions is crucial in topics like inverse functions, as only one-to-one functions have inverses. A function must be one-to-one for its inverse to also be a function.