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Let f:A→B and g:B→C be maps. Prove that if g◦f is a bijection, then f is...

Let f:A→B and g:B→C be maps. Prove that if g◦f is a bijection, then f is injective and g is surjective.*You may not use, without proof, the result that if g◦f is surjective then g is surjective, and if g◦f is injective then f is injective. In fact, doing so would result in circular logic.

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