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Question 10

 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) = 1Y(y) = fog2(y). Use one-one ness of f). 

Answer

Let fX  → Y be an invertible function.

Also, suppose f has two inverses (say g1 and g2).

Then, for all y ∈Y, we have:

Hence, f has a unique inverse.

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