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Math Help - Composition Function Proof

  1. #1
    Newbie Pi R Squared's Avatar
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    Question Composition Function Proof

    I am stuck on a composition function Proof.

    Let f:A-->B and g:B-->D. Prove that g 0 f is onto and g is 1-1, then f must be onto.

    I have ( and am not sure if it is correct...)

    Let f:A-->B and g:B-->D
    Let all d be and element of D and there exists and a in A such that f(a)=b.
    Then (g o f)(a)=g(f(a))
    =g(b)
    =d
    Therefore, g o f is onto


    Where I am a little confused is it looks like to me is that f:A-->B would not only have to be onto but also one to one...
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  2. #2
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    Quote Originally Posted by Pi R Squared View Post
    Let f:A-->B and g:B-->D. Prove that gof is onto and g is 1-1, then f must be onto.
    Note what is to be proven.

    If b\in B then g(b)\in D.
    Because g \circ f is onto \left( {\exists a \in A} \right)\left[ {g \circ f(a) = g(f(a)) = g(b)} \right].

    You know that g is one-to-one. So Finish.
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