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QUESTION
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,...
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.
