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Transform a function in terms of y

  1. Sep 9, 2008 #1
    In a calculus problem i'm doing I have to transform f(x) = 4x^2 - x^3 and y = 18 - 3x in terms of y.

    I did the second one and it's:

    x = - (y - 18) / 3

    But I can't transform the first one in terms of y :confused:
     
  2. jcsd
  3. Sep 9, 2008 #2
    You mean to find its inverse, right? But notice that since your first function is a quadratic one, it means that it does not have an inverse on its whole domain, since the quadratic functions are not one-to-one, so they don't have inverses. But you can work it out in two separate procedures, first saying that x is greater or equal to 0, and the secon one saying that x<0. Now this way our function is one-to-one in the restriction domains, so we can find its inverses by simply switching coordinates, that is x's and y's.
     
  4. Sep 9, 2008 #3

    Dick

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    It's a cubic, stupidmath. I wouldn't even try to solve it. Fiorella, if this is about that tangent problem you've posted in multiple copies, you don't need to invert the functions.
     
  5. Sep 9, 2008 #4
     
  6. Sep 9, 2008 #5

    Dick

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    If you learn how to do it, try and forget it as fast as you can. There is a solution, but it's amazingly useless in practical problems.
     
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