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 1

Let f : X → Y be an invertible function.
Then, there exists a function g : Y → X such that gof = IX and fog = IY
Here, f -1 = g.
Now, gof = IX and fog = IY
⇒ f -1 of = IX and fof -1= IY
Hence, f -1 : Y → X is invertible and f is the inverse of f -1
i.e., (f -1)-1 = f.