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Inverse of a transformation

  1. Oct 17, 2005 #1
    By some reason I can't access to Latex...

    Let be (x, y) = T(u,v) = (uv, v^u)

    So x = x(u,v) = uv
    and y = y(u,v) = v^u.

    I see that T is an injective function, but I can't find u = u(x, y). Can you help me?

    Thanks.
     
  2. jcsd
  3. Oct 17, 2005 #2

    EnumaElish

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    This involves a transcendental function. I'd try Mathematica see what it'd come up with, but I am not hopeful.
     
  4. Oct 17, 2005 #3
    Well let's drop that function, I would thank if you could provide any example of a transformation with its inverse.
     
  5. Oct 17, 2005 #4

    EnumaElish

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    Suppose x=uv, y=vu^2. Then v=x/u. Substitute into y=vu^2 to get y=xu; solve for u=y/x.
     
  6. Oct 17, 2005 #5
    OK, so u = u(x,y) = y/x and v = v(x,y) = (x^2)/y.

    Thanks, Enuma!
     
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