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Finding inverse of non-linear transformation

  1. Apr 1, 2008 #1
    Find the inverse of the (nonlinear) transformation from R^2 to R^2 given by



    3. The attempt at a solution

    - I'm really not sure what to do on this problem. We haven't seen any problems even similar to it in class, so I'm looking for help on it.
  2. jcsd
  3. Apr 1, 2008 #2


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    So y= u/3. Put that into the second equation: v= 3x^7- 6(u/3)= 3x^7- 2u.
    Solve that for x.

  4. Apr 1, 2008 #3
    well, that was much easier than I thought it would be. Can you explain to me why that is the inverse?
  5. Apr 1, 2008 #4


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    What do you think an inverse is? You had u= 3y, v= 3x^7- 6y and you said the answer must be in the form x=, y= . I reduce the two equation to that form, solving for x and y.

    Perhaps more specifically, if you start with (x, y) and apply the original tranform, you get (3y, 3x^7 - 6y). Now what happens if you apply the tranformation x= ((v+2u)/3)^(1/7, y= u/3? Since u= 3y, the second gives y= (3y)/3= y immediately. Since u= 3y and v= 3x^7- 6y, the x= ((3x^7- 6y+ 2(3y))/3)^(1/7)= ((3x^7/3)^(1/7)= (x^7)^(1/7)= x.
    That's what an inverse is supposed to do.
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