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)}

Next: Example 28 (b) → Ask a doubt

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular