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

Question

Philoid · Accepted 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^-1of = 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.