< mathematics > A function f : A -> B is surjective or onto or a surjection if f A = B. I.e. f can return any value in B. This means that its image is its codomain .
Only surjections have right inverses , f' : B -> A where f (f' x) = x since if f were not a surjection there would be elements of B for which f' was not defined.
See also bijection , injection .
(1995-05-27)