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Homework Help: Subset math help

  1. Aug 21, 2010 #1
    1. The problem statement, all variables and given/known data

    F : R-{1/3} ---> R-{0}
    F(x) = 1/(3x-1)

    to show R-{0} [tex]\subseteq[/tex] image of F

    for any y in R-{0}, if we try to solve y=1/(3x-1), we find x=(1+y)/3y,

    F((1+y)/3y)=y

    2. Relevant equations

    R is real number

    3. The attempt at a solution

    so, if (1+y)/3y are the values for x in R-{0} such that F((1+y)/3y)=y

    but i don't understand, how is that showing R-{0} [tex]\subseteq[/tex] image of F

    explain to me please
     
  2. jcsd
  3. Aug 21, 2010 #2

    radou

    User Avatar
    Homework Helper

    Re: subset

    You have shown that if y is in R\{0}, then it is in the image of F, too, since for such a number y there exists a number x = (1 + y) / 3y whose image under F is y. (btw the image of F is defined as {F(x) : x is in R\{1/3}})
     
  4. Aug 21, 2010 #3
    Re: subset

    thanks, i get it now ^^
     
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