(5) Let ƒ : A → B and g : B → C, where f and g are functions and A, B, and C are sets. (a) Prove that if go f : A → C is invertible then g must be surjective and f must be in- jective. (b) Find functions f and g and sets A, B, and C which demonstrated gof can be invert- ible, even if g is not injective and f is not surjective.

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A: Please see the below picture for detailed solution.

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