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What is the inverse of the function

  1. May 3, 2006 #1
    I'm running out of ideas:


    Does someone here now how to solve for [tex]y[/tex] in terms of [tex]x[/tex]?
    Last edited: May 3, 2006
  2. jcsd
  3. May 3, 2006 #2


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    Homework Helper

    [tex]y^3 + \frac{a}{b}y - \frac{x}{b} = 0[/tex]

    Two ways :

    1) Substitute [tex]y = z - \frac{a}{3bz}[/tex]. Form a quadratic in [tex]z^3[/tex], solve for z and find y.

    2) Compare equation to the trig identity [tex]cos^3 \theta - \frac{3}{4}\cos\theta - \frac{1}{4}\cos 3\theta = 0[/tex] while letting [tex]y = m\cos\theta[/tex] then comparing coefficients. With this method, if you have to compute the arccosine of a value greater than one in magnitude, use the identity [tex]\cos i\theta = \cosh \theta[/tex]

    These are methods used to solve the general cubic in radicals/trig/hyperbolic trig ratios when the second degree term is missing (or has been eliminated).
    Last edited: May 3, 2006
  4. May 9, 2006 #3
    Last edited: May 9, 2006
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