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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

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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.

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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.