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Condition for a function to be injective

  1. Oct 2, 2012 #1

    dpa

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    1. The problem statement, all variables and given/known data
    Do all the preimages on X need to have a (and of course I know only one but) image in Y for the f:x->y to be injective?
    IS THE FOLLOWING FUNCTION INJECTIVE SINCE ONE ELEMENT OF FIRST DOES NOT HAVE ANY IMAGE
    attachment.php?attachmentid=51453&stc=1&d=1349212542.png

    2. Relevant equations



    3. The attempt at a solution
    Thank You.
     

    Attached Files:

  2. jcsd
  3. Oct 2, 2012 #2

    HallsofIvy

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    Staff Emeritus
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    The way you have shown it, f is not a function from X to Y.
     
  4. Oct 2, 2012 #3

    dpa

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    Thank you.
     
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