surjective
A function $f:X\to Y$ is called surjective^{} or onto if, for every $y\in Y$, there is an $x\in X$ such that $f(x)=y$.
Equivalently, $f:X\to Y$ is onto when its image is all the codomain:
$$\mathrm{Im}f=Y.$$ 
Properties

1.
If $f:X\to Y$ is any function, then $f:X\to f(X)$ is a surjection. That is, by restricting the codomain, any function induces a surjection.

2.
The composition^{} of surjective functions (when defined) is again a surjective function.

3.
If $f:X\to Y$ is a surjection and $B\subseteq Y$, then (see this page (http://planetmath.org/InverseImage))
$$f{f}^{1}(B)=B.$$
Title  surjective 
Canonical name  Surjective 
Date of creation  20130322 12:32:48 
Last modified on  20130322 12:32:48 
Owner  drini (3) 
Last modified by  drini (3) 
Numerical id  7 
Author  drini (3) 
Entry type  Definition 
Classification  msc 0300 
Synonym  onto 
Related topic  TypesOfHomomorphisms 
Related topic  InjectiveFunction 
Related topic  Bijection 
Related topic  Function 
Related topic  OneToOneFunctionFromOntoFunction 
Defines  surjection 