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Inverse for cubic function

  1. Aug 22, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the inverse of f(x)=ln(x^3-3x^2+3x-1)

    2. Relevant equations

    n/a

    3. The attempt at a solution

    y=ln(x^3-3x^2+3x-1)
    x=ln(y^3-y^2+3y-1)
    e^x=(y^3-y^2+3y-1)

    i looked around for inverse of cubic functions and i found a monster of a formula:
    http://www.math.vanderbilt.edu/~schectex/courses/cubic/
    i really hope i missed something to find the inverse
     
  2. jcsd
  3. Aug 22, 2013 #2

    D H

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    Staff Emeritus
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    You dropped a very important factor of three in going from y=ln(x^3-3x^2+3x-1) to x=ln(y^3-y^2+3y-1).

    Those factors of three should suggest something. Hint:Look at Pascal's triangle.
     
  4. Aug 22, 2013 #3
    whoops
    $$y=ln(x^3-3x^2+3x-1)$$
    $$y=ln(x-1)^3$$
    $$x=ln(y-1^3)^3$$
    $$e^x=(y-1)^3$$
    $$y=e^x/3+1$$
    ty for the hint
     
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