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Question 12

Let f: X → Y be an invertible function. Show that the inverse of f –1 is f, i.e., (f–1)–1 = f.

Answer

Let fX → Y be an invertible function.

Then, there exists a function gY → X such that gof = Ix and fog = Iy

Here, f-1 = g.

Now, gof = Ix and fog = Iy

⇒ f-1of = Iand fof-1=  Iy

Hence, f-1Y → X is invertible and f is the inverse of f-1

i.e., (f-1)-1 = f.

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