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Math Help - Finding the inverse of a function with two of the same variables

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    Finding the inverse of a function with two of the same variables

    f(x) = 3x3 - x. If h(x) is the inverse of f(x) then h'(-2) =

    Ok this is what I did:
    1. Switched f(x) and replaced it with y, even though they're the same thing, but it's easier to see.
    y = 3x3 - x

    2. Switched the x and y variables in order to find the inverse.
    x = 3y3 - y

    3. Multiply both sides by natural log.
    ln(x) = ln(3y3 - y)

    4. Distributed the natural log on the other side.
    ln(x) = ln(3y3) - ln(y)

    5. Use the log property, where subtracting two logs will mean dividing it.
    ln(x) = ln(3y3)/ln(y)

    6. Brought the exponent into the front.
    ln(x) = 3ln(3y)/ln(y)

    But then... I think I'm just experimenting and moving stuff around...
    I don't think I'm really sure if I'm getting anywhere with this.
    At first I stopped at step #2, and tried using natural log to see if it'll work.

    But so far, I still have all 'y' on one side.
    Anyone think they can help me out please?
    Thanks
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    Re: Finding the inverse of a function with two of the same variables

    Quote Originally Posted by Chaim View Post
    f(x) = 3x3 - x. If h(x) is the inverse of f(x) then h'(-2) =
    You want to find h'(-2)=\frac{1}{f'(h(-2))}.

    It is clear that f(-1)=-2 so h(-2)=-1.
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    Re: Finding the inverse of a function with two of the same variables

    Quote Originally Posted by Plato View Post
    You want to find h'(-2)=\frac{1}{f'(h(-2))}.

    It is clear that f(-1)=-2 so h(-2)=-1.
    Oh wow, that makes more sense now.
    So basically to find the inverse, you could just place under the denominator of 1 right?
    Then after that you find out the derivative of f, which is 9x2 - 1
    Then I plug in the -1, which makes the denominator = -10 right?

    Then it would be -1/10?
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    Re: Finding the inverse of a function with two of the same variables

    Quote Originally Posted by Chaim View Post
    Then after that you find out the derivative of f, which is 9x2 - 1
    Then I plug in the -1, which makes the denominator = -10 right?
    Then it would be -1/10?
    Well no.
    f'(x)=9x^2-1 so f'(-1)=8.
    Last edited by Plato; March 14th 2013 at 03:11 PM. Reason: typo
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    Re: Finding the inverse of a function with two of the same variables

    Quote Originally Posted by Plato View Post
    Well no.
    f'(x)=27x^2-1 so f'(-1)=26.
    ??? In the original post, the function [tex]f(x)= 3x^3- x[/quote] which has derivative f'(x)= 9x^2- 1, as Chaim said, not 27x^2- 1.
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