Onto and Into Functions

If the range of a function is equal to the co-domain then the function is called an onto function. Otherwise it is called an into function.

In f:A→B, the range of for the image set f(A) is equal to the co-domain B i.e. f(A) = B then the function is onto.

For an onto function for each element (image) in the co-domain, there must be a corresponding element or elements (pre-image) in the domain.

Another name for onto function is surjective function.

Definition

A function f is onto if to each element bin the co-domain, there is at least one element a in the domain such that b = f(a).