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The inverse of X^3/X^2+1

  1. Dec 5, 2011 #1
    Hello,

    I have been working on this problem for a while now and can't seem to get it into a forum which would isolate x, which would then allow me to sub y and find the inverse.

    The problem is x^3/x^2+1

    Can anyone help me with this? I am utterly stuck

    I have dealt with a similar problem before.... x+1/x-1.... the trick for that was to express the statement twice, once with x-1 in the numerator and x+2 in the numerator..... which would cancel the first statement and isolate x etc.

    However, this problem we have a cube and a square in the numerator and the denomator.

    Can someone please help?

    Thanks
     
  2. jcsd
  3. Dec 5, 2011 #2

    Mark44

    Staff: Mentor

    Presumably you mean f(x) = x3/(x2 + 1). What you wrote would be interpreted as (x3/x2) + 1 = x + 1.
    The similar problem was y = (x + 1)/(x - 1), I'm pretty sure.
    (x + 1)/(x - 1) = (x - 1 + 2)/(x - 1) = (x - 1)/(x - 1) + 2/(x - 1) = 1 + 2/(x - 1). Is this what you're talking about? If so, it's fairly easy to solve the equation y = 1 + 2/(x - 1) for x.
    Solving the equation y = x3/(x2 + 1) for x is possible, but pretty difficult.

    Multiply both sides by x2 + 1:
    y(x2 + 1) = x3

    Expand the left side and bring all terms to the left side:
    yx2 + y - x3 = 0

    Rearrange by powers of x:
    -x3 + yx2 + y = 0

    Solving for x amounts to finding the solutions of this cubic equation, a technique that has been around for a long time, but isn't usually taught.
     
  4. Dec 5, 2011 #3
    Thanks so much,

    I was afraid I'd be left in this form. Oh well, must use Cardano's equation now....

    Thankyou very much
     
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