Eén-op-één-functies en hun inverse functies

A one-to-one function is a function where each input maps to a unique output.

If two distinct inputs lead to the same result, the function is not one-to-one.

This often happens with certain functions in which both positive and negative inputs produce the same output, violating the one-to-one rule.

Restricting the domain, such as limiting inputs to non-negative values, can restore this property.

A one-to-one function passes the horizontal line test, meaning no horizontal line crosses the graph of a one-to-one function more than once.

Only one-to-one functions qualify for an inverse. The notation “f inverse of x”, does not mean “f raised to the negative first power”. Instead, an inverse reverses the process, returning each output to its input.

This visually confirms that the one-to-one function’s domain becomes the inverse’s range, and the range becomes the domain. When a function and its inverse are composed, the operations cancel out and produce x.

In a school database, each student ID links to one student only. This forms a one-to-one function where each input has a single, distinct output.