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Homework Help: Inverse function help

  1. May 6, 2008 #1
    Ok, I decided to review basic algebra since I haven't done anything with it in like, forever. I came across an inverse function problem that I can't get the right answer.

    the equation is:

    y = cuberoot(x+sqrt(1+x^2)) + cuberoot(x-sqrt(1+x^2))

    I tried replacing X with Y, and solving for Y
    and getting rid of the cube roots by cubing both sides
    X^3 = y + sqrt(1+y^2) + y - sqrt(1+y^2)
    simplifying a bit (the square roots go away)
    x^3 = 2y
    y = (1/2)x^3

    Yet the book I'm using says the answer is y=(1/2)(3x+x^3)

    What did I do wrong?
  2. jcsd
  3. May 6, 2008 #2

    Shooting Star

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    Homework Helper

    (a+b)³ =/= a³ + b³, as you have done.

    Use (a+b)³ = a³ + b³ +3ab(a+b).

    Start with y = a+b, and cube both sides. If you put a+b=y again, the result comes quickly,
  4. May 6, 2008 #3
    thanks, I think I got it. Man, a few years ago I could have done this, but now? I feel like a 9th grader again.
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