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Providing Proof about Functions

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Let f: X--> Y and g: Y-->Z be functions. Show that if g o f is injective, then f must be injective. Is it true that g must also be injective? Show that if g o f is surjective, then g must be surjective. Is it true that f must also be surjective?

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Recall that a function f:X-->Y is called injective, if for any elements x and x' from X, the equality f(x)=f(x') implies that x=x'. f is called surjective if for any element y from Y there exists an element x from X such that f(x)=y.

Let gf: X-->Z be injective, and let x, x' be elements of X such that ...

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This solution helps with proof about functions.

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