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

1.	Let f:X → Y be an invertible function. Show that fhas unique inverse.(Hint:suppose g1 and g2 are twoinverses of f. Then for all y ∈Y,fog1(y)= IY(y) = fog2(y).Use one-one ness of f).
Answer» 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).

Let f:X → Y be an invertible function. Show that fhas unique inverse.(Hint:suppose g1 and g2 are twoinverses of f. Then for all y ∈Y,fog1(y)= IY(y) = fog2(y).Use one-one ness of f).

Answer»

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).