Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is the inverse of the function

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

    [tex]x=ay+by^3[/tex]

    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

    Curious3141

    User Avatar
    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What is the inverse of the function
  1. Inverse functions (Replies: 3)

  2. Inverse functions (Replies: 3)

  3. Inverse function (Replies: 12)

  4. Inverse of a function (Replies: 6)

  5. Inverse function (Replies: 5)

Loading...