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)}

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.

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