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Operations of Functions : Injective, Surjective and Bijective

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Let f: A ?> B and g: B ?> C be functions.
a) Suppose that f and g are injective. Show that g o f is injective.
b) Suppose that f and g are surjective. Show that g o f is surjective.
c) Suppose that f and g are bijective. Then g o f is bijective by parts a) and b). Show that (gof)^-1 = f^-1 o g^-1.

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Solution Summary

Pointwise Operations ( Composition and Inverse ) of Injective, Surjective and Bijective Functions are investigated. The solution is detailed and well presented.

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