Question

Let f: X → Y be an invertible function. Show that f has unique inverse.

(Hint: suppose g₁ and g₂ are two inverses of f. Then for all y ∈ Y,

fog₁(y) = I_Y(y) = fog₂(y). Use one-one ness of f).

Answer 1

Let f: X → Y be an invertible function.

Also, suppose f has two inverses (say_).

Then, for all y ∈Y, we have:

Hence, f has a unique inverse.