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 x_1 \neq x_2 implies that f(x_1) \neq f(x_2).

An injective function f has a well-defined partial inverse f^{-1}. If y is an element of the image set of f, then there is at least one input x such that f(x) = y. If f is injective then this x is unique and we can define f^{-1}(y) to be this unique value. We have f^{-1}(f(x)) = x for all x in the domain.

A strictly monotonic function is injective, since in this case x_1 < x_2 implies that f(x_1) < f(x_2).

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