Question:
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 f: X → Y be an invertible function.

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

Here, f^-1 = g.

Now, gof = I_xand fog = Iy

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

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