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Homework Help: HELP I do not understand!

  1. Mar 22, 2008 #1
    HELP!!! I do not understand!

    1. The problem statement, all variables and given/known data
    Define f(x)=2x, x is rational and x+3 when x is irrational. Find all points where g(x) is continuous and prove continuity at these points

    2. Relevant equations
    From analysis homework and using the real definition of continuity

    3. The attempt at a solution

    Graphing g(x) I can see that the only point that will be continuous will be at x=3, how would you show using the definition that this point is continuous. Also is this the only point. I have been struggling, please help a girl in distress. lol
  2. jcsd
  3. Mar 22, 2008 #2


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    Science Advisor
    Homework Helper

    … 'tis I … tiny-tim! …

    :smile: … don't worry that pretty little head … :smile:

    Just choose an epsilon, and find a delta such that f(3 + x) - 6 < epsilon, for all x < delta, and all your worries will go away! :smile:
  4. Mar 22, 2008 #3
    so I just solve it like a limit problem? Thank you so much, I just knew someone would help a girl in distress lol.
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