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Is there a relationship between

  1. Jan 20, 2009 #1
    Let's say I setup the equation:

    [tex] f(x) = f(x) [/tex]

    Now, let's say I add two independent real-valued variables, a and b, to the equation, where either a is a function of b and x or b is a function of a and x, making the statement true at all times:

    [tex] f(x) = af(x+b)[/tex]

    Finding a' and b' we have:

    [tex] a' = -\frac{f'(x+b)f(x)}{f(x+b)^2}[/tex]

    [tex] b' = -f^{-1}'(\frac{f(x)}{a})\frac{f(x)}{a}[/tex]

    My question is, is there a distinct relationship between a' and b'?
    Last edited: Jan 20, 2009
  2. jcsd
  3. Jan 20, 2009 #2
    I think I got it, they are reciprocals, but they don't readily cancel out.
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