Answer :

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

Then, there exists a function g: Y → X such that gof = I_{x} and fog = I_{y}.

Then, f^{-1} = g.

Now, gof = I_{x} and fog = I_{y}

⇒ f^{-1}of = I_{x} and fof^{-1} = I_{y}

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

Therefore, (f^{-1})^{-1} = f.

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