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Implicit function on functions composed of itself

  1. Jan 13, 2007 #1
    Suppose F(x, y) is C1. F(0, 0) = 0. What conditions on F will guarantee that the equation F(F(x, y), y) = 0 can be solved for y as a C1 function of x near (0, 0) ?

    would it simply be dF/dy not equal 0 ?
  2. jcsd
  3. Jan 13, 2007 #2
    Use the implicit function theorem. Seems you are on the right track, but F is a composition of F and y, so you would have to use the chain rule to right out dF/dy properly.
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