A function f:A→X is said to be onto if it maps some element of the domain A onto every element of the range X. That is, its image is equal to its range.
In symbols, "f[A]=X", or
∀ x in X
∃ a in A
For example, the function f(x,y) = x2 - y2 is onto R,
but f(x,y)=x2+y2 is not (it takes on only non-negative values).
A function which is onto is also said to be surjective.