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What kind of equation is this and how could I solve it?

  1. Jun 19, 2013 #1
    1. The problem statement, all variables and given/known data
    I was wondering if anyone can tell me about this equation:

    f(x)=f(y)+cx

    How can I select points for this equation and graph it? What values are constant and what values are changing? Thanks

    2. Relevant equations

    f(x)=f(y)+cx

    3. The attempt at a solution

    Well... maybe choose a fixed value for y and for c?
     
  2. jcsd
  3. Jun 19, 2013 #2

    LCKurtz

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    What happens if you put y = 0?

    [Edit-Added]Are you sure you have stated the problem completely and correctly? Putting y=0 gives f(x) = f(0) + cx. Putting y = t gives f(x) = f(t) + cx. Subtracting those says f(0) = f(t) so f is constant. But that doesn't work unless c = 0.
     
    Last edited: Jun 19, 2013
  4. Jun 19, 2013 #3
    :smile:OK, that's a possibility, thanks LCKurtz
     
  5. Jun 19, 2013 #4

    LCKurtz

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    Make sure you notice my edited comment.
     
  6. Jun 19, 2013 #5
    Oh thanks for that message, I did not see your edited response...You are right, there is more!!! :smile: The equation is [itex]\alpha[/itex]^(-1)(t)=[itex]\alpha[/itex]^(-1)(m)+(1/2[itex]\pi[/itex])(β)(t). This is for the running of the couplings, haven't done any of this stuff until this summer... Hope you can shed some light!
     
  7. Jun 19, 2013 #6

    haruspex

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    I assume you want to arrive at y as a function of x, y=y(x) (or in the revised version m = m(t)).
    Please clarify what alpha is here. Judging from the original post it is an arbitrary unknown function. If so, I see no hope of saying much about m(t). If you assume it's invertible then you can show m(0) = 0.
     
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