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Prove a delta function identity

  1. Feb 18, 2008 #1

    I'm stuck with the last proof I need to do

    1. The problem statement, all variables and given/known data

    I need to prove that f(x)delta(g(x)) = f(x) delta (x-x0)/abs(g'(x))
    By delta I mean the Dirac delta function here. (I'm new to this forum, so i don't know how to write it all nicely like so many of you do!)

    2. Relevant equations

    3. The attempt at a solution

    First of all, of course, I put all of that in an integral. And what I've done so far is just replace g(x) = u so that dx=du/g'(x) It looks promising because I have the g'(x) dividing everything, and if I could somehow use the identity that says that delta(kx) = delta/abs(k) I could almost have it but it seems to me that that identity only works for k a constant and g'(x) is not. Also, I have no idea what to do with my f(x). Can I express it as f(g^-1 (x))??? It seems just very weird to me. So, basically I'm stuck there. Any help would be great!!
  2. jcsd
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