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Let M={7,8,9}. Determine which of the following functions is invertible for f:M→M.(a) f = {(7,7),(8,8),(9,9)}(b) f = {(7,8),(7,9),(8,9)}(c) f = {(8,8),(8,7),(9,8)}(d) f = {(9,7),(9,8),(9,9)}I got this question in an internship interview.This is a very interesting question from Composition of Functions and Invertible Function in division Relations and Functions of Mathematics – Class 12

Answer»

Correct option is (a) f = {(7,7),(8,8),(9,9)}

For explanation: The function f = {(7,7),(8,8),(9,9)} is INVERTIBLE as it is both one – one and ONTO. The function is one – one as every element in the domain has a distinct image in the co – domain. The function is onto because every element in the codomain M = {7,8,9} has a PRE – image in the domain.



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