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Math Help - Proof about composites

  1. #1
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    Proof about composites

    I need help proving the following:

    Let f: A--> B and g: B--> C be functions. Prove that if gf is injective, then f is injective. Also, prove that if gf is surjective, then g is surjective.
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  2. #2
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    Quote Originally Posted by page929 View Post
    I need help proving the following:
    Let f: A--> B and g: B--> C be functions. Prove that if gf is injective, then f is injective. Also, prove that if gf is surjective, then g is surjective.
    I see that you have nine postings.
    By now you should understand that this is not a homework service
    So you need to either post some of your work on a problem or explain what you do not understand about the question.
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  3. #3
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    I understand that g◦f is g(f(x)). So if g◦f is injective then every element of A matches to an element of C. Then every element of A has to match to B and therefore f is injective. And for the other part, since g◦f is surjective then every element in C is the image of something in A. Then g is surjective since every element in C is the image of something in B and every element in B is the image of something in A.

    I don't know if this will make any since.
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  4. #4
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    Start this way. If f(a)=f(b) can you use the given to show that a=b?
    That shows f is injective.

    What does g\circ f(a)=g\circ f(b) imply and WHY?
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