Q. 123.9( 29 Votes )
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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