Ex 1.3, 12 - Let f be invertible. Show inverse of f-1 is f - Invertible functions: Proofs

Ex 1.3, 12 - Chapter 1 Class 12 Relation and Functions - Part 2

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 1.3, 12 Let f: X Y be an invertible function. Show that the inverse of f 1 is f, i.e.,(f 1) 1 = f. Let f: X Y be an invertible function. Let g: Y X be the inverse of f, i.e. g = f 1 So, gof = IX and fog = IY. Since g is inverse of f, it is also invertible Let g 1 be the inverse of g So, g 1og = IX and gog 1 = IY f 1of = IX and fof 1= IY Hence, f 1: Y X is invertible and f is the inverse of f 1 i.e., (f 1) 1 = f.

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

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.