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Homework Help: Composite function

  1. Feb 15, 2010 #1
    1. The problem statement, all variables and given/known data
    let A,B,C be sets, and let f : A--> B and g : B--> C be functions. The composite function denoted by g o f is a function from A to C defined as follows:

    2. Relevant equations

    g o f(x)=g(f(x)) for every x in A.

    Prove that if g o f is one-to one, then f is one-to one
    Prove that is g o f is onto, then g is onto

    3. The attempt at a solution
    I really don't know how to approach this problem. I didnt things similar with binary structures determining if they are an isomorphism by not familiar with composite functions
  2. jcsd
  3. Feb 15, 2010 #2
    I think I know how to approach it....check me if I'm right though

    check if its one-to-one and onto

    if it is one-to-one that implies if f(a)=f(b) then a=b
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