Onto function: Learn what an onto function

Learn what an onto function or a surjective function is, how to find the number of onto functions, and how to prove whether a function is surjective. See examples, properties, and related articles on surjective functions. An onto function , also known as a surjective function , is a type of function where every element in the co-domain is mapped to at least one element in the domain. In other words, an onto function covers the entire codomain, ensuring that every possible output value is achieved by some input value. A function f : A -> B is said to be an onto function if every element in B has a pre-image in A. That is, a function f is onto if for each b ∊ B, there is at least one element a ∊ A, such that f (a) = b. This is same as saying that B is the range of f. An onto function is also called a surjective function . In the above figure, f is an onto ... In mathematics, a surjective function (also known as surjection, or onto function / ˈɒn.tuː /) is a function f such that, for every element y of the function's codomain, there exists at least one element x in the function's domain such that f(x) = y.