1.7 Types of Functions · Part 2

F F P P P P P P P Fig. . A function f : ® is called many-one function if two or more elements of A have same image in B . In other words, a function f : ® is called many-one if f it is not one–one. Illustration Let A = { , , , } and B = { a , b , c }, f = {( , a ), ( , a ), ( , b ), ( , c )} Then f is a function from A to B in which different elements and of A have the same image a in B . Hence f is a many – one function. . . Onto function In a mobile phone assume that there are persons in the contact. If every person in the contact receives a call, then the function representing making calls will be onto . (Fig. . ) A function f : ® is said to be onto function if the range of f is equal to the co-domain of f . In other words, every element in the co-domain B has a pre-image in the domain A . An onto function is also called a surjection .