# Injective function

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In mathematics, an **injective function** or **one-to-one function** or **injection** is a function which has different output values on different input values: *f* is injective if implies that .

An injective function *f* has a well-defined partial inverse . If *y* is an element of the image set of *f*, then there is at least one input *x* such that . If *f* is injective then this *x* is unique and we can define to be this unique value. We have for all *x* in the domain.

A strictly monotonic function is injective, since in this case implies that .