Injective function

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.