Results 1 to 4 of 4
Like Tree3Thanks
  • 1 Post By chiro
  • 2 Post By JJacquelin

Math Help - Inverse function

  1. #1
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    509
    Thanks
    139

    Inverse function

    I have been working on a project where I have a function F(x) which is closely related to a function G(x). The function G(x) has been well studied already and tools exist for using it. To make the equations I derive for F(x) useful I wanted to convert them into G(x) so that people can evaluate things for F(x) using the tools that already exist for G(x)
    So far I derived their relationship
    r\cdot F(x)+ c= G(x)

    So for example if I had this equation to find an important number B
    B= F(5)-F(y)

    I could turn it into
    B= \frac{G(5)-c}{r}-\frac{G(y)-c}{r}


    B= \frac{G(5)-G(y)}{r}

    And use the tools that exist for G(x) to find B for any y

    But I am stuck when it comes to their inverse functions. As an example of this I have derived the equation
    L=F^{-1}(y-0.5)

    I am confused about how I can use the relationship r\cdot F(x)+ c= G(x) to get L in terms of the inverse function of G. I am not even sure if this is possible to do
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Inverse function

    Hey Shakarri.

    One method I think you should investigate is the rule of the derivative of an inverse function (in terms of its non-inverse) and the chain rule of differentiation.

    If you combine those together you should get a Taylor series for your function and if its in a simple enough form (or recognizable form), then you can substitute the appropriate elementary functions in.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2011
    Posts
    234
    Thanks
    53

    Re: Inverse function

    Hi !
    if I well understand, you previously compute the values of c and r so that (G(x)-c)/r be a good approximation for F(x).
    Then, you want to compute x so that F(x)=y , given y. (i.e. the inverse function of F)
    G(x)=c+r*F(x) = c+r*y
    Hence : x = value of the inverse function of G, for the argument X=(c+r*y)
    That is : x = F^(-1){y} = G^(-1){X} where X=c+r*y
    Thanks from Shakarri and topsquark
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    509
    Thanks
    139

    Re: Inverse function

    Ah thank you, I was wondering about that solution but I was really unsure about inverse functions. Anyway now you have derived it and it works with all the cases which I can think of with trivial solutions so it must be correct
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 16th 2013, 12:38 AM
  2. function composition and inverse function
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: November 10th 2009, 12:18 PM
  3. Replies: 2
    Last Post: September 22nd 2009, 08:29 PM
  4. Replies: 0
    Last Post: July 19th 2008, 08:06 PM
  5. Replies: 4
    Last Post: March 17th 2008, 09:45 PM

Search Tags


/mathhelpforum @mathhelpforum