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.

A strictly monotonic function is injective, since in this case $x_{1}<x_{2}$ implies that $f(x_{1})<f(x_{2})$.

See also

• Bijective function
• Surjective function