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Math Help - composition of functions

  1. #1
    Member oldguynewstudent's Avatar
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    composition of functions

    I am so rusty at this:
    Theorem: Let f: A \longrightarrowB and g:B \longrightarrowC.

    Prove that if f and g are onto, then g \circf is onto.

    Since g is onto \forall c \in C \exists b \in B such that g(b) = c.

    Since f is onto \forall b \in B \exists a \in A such that f(a) = b.

    Therefore \forall c \in C \exists a \in A such that g(f(a)) = c.
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  2. #2
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    It is a bit rough for my taste, but it works.
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