Q12 of 107 Page 18

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

It is given that f: X → Y be an invertible function.

Then, there exists a function g: Y → X such that gof = Ix and fog = Iy.


Then, f-1 = g.


Now, gof = Ix and fog = Iy


⇒ f-1of = Ix and fof-1 = Iy


Thus, f-1: Y→X is invertible and f is the inverse of f-1.


Therefore, (f-1)-1 = f.


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