Let F A B Be An Arbitrary Function A Prove That If F Is A Bijection And Hence

5.6.15. Let f : A –> B be an arbitrary function.

(a) Prove that if f is a bijection (and hence invertible), then f^-1(f(x)) = x for all x belonging to A, and f(f^-1(x)) =

x for all x belonging to B.

(b) Conversely, show that if there is a function g : B –> A, satisfying g(f(x)) = x for all x belonging to A, and

f(g(x)) = x for all x belonging to B, then f is a bijection, and f^-1 = g.

 

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