1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Dec 5, 2011 #1

    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?

  2. jcsd
  3. Dec 5, 2011 #2


    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook