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B Let b ∈ B Put a = g(b) So (b,a) ∈ g, so (b,a) = (f(c),c) for some c ∈ A We must have c = a, so b = f(a), ie b = f(g(b)), as required g f = 1 A Let a ∈ A Then (f(a),a) ∈ g, so g(f(a)) = a, as required Images and preimages 53 Definition Let f A → B be a function For S ⊆ B we define the inverse image or preimageTitle INBZASDINRUpdf Author kkasprzak Created Date AM116 = H > B R G B D g Z F b g g h _ h e h ` d b y m g b \ _ j k b l _ l " K \ B \ Z g J b e k d b", L h f 53, K \I 1 1, F _ o Z g b a Z p b y, _ e _ d l j b n Analysis If Int A Bf X Dx Le Int A Bg X Dx Is It True F C Le G C For Some C In A B Mathematics Stack Exchange ~fBA Xg[g C[