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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 .