1.7 Types of Functions

. Types of Functions In this section, we will discuss the following types of functions with suitable examples. (i) one – one (ii) many – one (iii) onto (iv) into . . One – one function Let us assume that we have a cell phone with proper working condition. If you make a usual call to your friend then you can make only one call at a time (Fig. . ). If we treat making calls as a function, then it will be one - one. A function f : ® is called one – one function if distinct elements of A have distinct images in B . A one-one function is also called an injection . Equivalently, If for all a a Î , f a f a implies a , then f is called one – one function . Illustration A = { , , , } and B = { a , b , c , d , e } (i) Let f = {( , a ), ( , b ), ( , d ), ( , c )} In Fig. . , for different elements in A , there are different images in B . Hence f is a one – one function. (ii) Let g = {( , b ), ( , b ), ( , c ), ( , e )} g is a function from A to B such that g g = , but ¹ . Thus two distinct elements and in the first set A have same image b the second set in B (Fig. . ). Hence, g is not a one–one function. . . Many – one function In a theatre complex three films F , F , F are shown. Seven persons ( P to P ) arrive at the theatre and buy tickets as shown (Fig. . ). If the selection of films is considered as a relation, then this is a function which is many–one, since more than one person may choose to watch the same film. # # # Fig. . D E Calls Friends e Fig. . f e Fig. . g Persons Films F