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

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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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