Surjective function
High school
A function is surjective if every element of the codomain is an output for some input.
Undergraduate
A function $f : X \to Y$ is surjective if for every $y \in Y$ there exists $x \in X$ such that $f(x) = y$.
Properties
- A function is surjective if and only if its image equals its codomain, so whether it is surjective depends on the choice of codomain.