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G of f injective, but g not injective

  1. Sep 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Give an example of a map f:A[tex]\rightarrow[/tex]B and a map g:B[tex]\rightarrow[/tex]C where g of f is injective but g is not injective.


    2. Relevant equations



    3. The attempt at a solution
    I'm not really sure what they are asking for.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 29, 2009 #2

    Mark44

    Staff: Mentor

    In a nutshell, find two functions, f and g, so that g [itex]\circ [/itex] f is one-to-one, but f [itex]\circ [/itex] g is not.
     
  4. Sep 29, 2009 #3
    So it's basically just guess and check?
     
  5. Sep 29, 2009 #4
    It doesn't have to be. Think about arranging it so that g is injective on the image of f but not on the entire domain of g.
     
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