![Example 28 - Chapter 1 Class 12 Relation and Functions - Part 2](https://d1avenlh0i1xmr.cloudfront.net/5fc07600-7858-4a36-a1fd-46a2d6ce16cd/slide76.jpg)
Examples
Last updated at April 16, 2024 by Teachoo
Example 28 Let S = {1, 2, 3}. Determine whether the functions f : S → S defined as below have inverses. Find f–1, if it exists. (a) f= {(1, 1), (2, 2), (3, 3)} A function has inverse if it is one-one and onto Check one one f = {(1, 1), (2, 2), (3, 3)} Since each element has unique image, f is one-one Check onto Since for every image, there is a corresponding element, ∴ f is onto. Since function is both one-one and onto it will have inverse f = {(1, 1), (2, 2), (3, 3)} f-1 = {(1, 1), (2, 2), (3, 3)}