Question

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 1

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.