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Math Help - how to factor a polynomial to the yth degree

  1. #1
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    how to factor a polynomial to the yth degree

    How would I go about finding the inverse of the function f(x)=3+x+e^x

    ?


    I can rewrite the forumla interchanging the x and y variables to obtain

    x = 3+y+e^y

    but I'm not sure where to go from here.

    thanks!
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    Re: how to factor a polynomial to the yth degree

    1st you should find x in terms of y as x=g(y), then switch x & y positions and check domain and range values.
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    Re: how to factor a polynomial to the yth degree

    Quote Originally Posted by kingsolomonsgrave View Post
    How would I go about finding the inverse of the function f(x)=3+x+e^x

    ?


    I can rewrite the forumla interchanging the x and y variables to obtain

    x = 3+y+e^y

    but I'm not sure where to go from here.

    thanks!
    You will not be able to get an explicit equation y in terms of x, because of the fact that y is both "inside" a polynomial function and a transcendental function.
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    Re: how to factor a polynomial to the yth degree

    kingsolomonsgrave, where did you get this question from?
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    Re: how to factor a polynomial to the yth degree

    Quote Originally Posted by Prove It View Post
    You will not be able to get an explicit equation y in terms of x, because of the fact that y is both "inside" a polynomial function and a transcendental function.
    thanks!
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    Re: how to factor a polynomial to the yth degree

    Quote Originally Posted by Vlasev View Post
    kingsolomonsgrave, where did you get this question from?
    I got this from section 1.6 of James Stewart's 7th edition of Calculus

    this one: http://www.amazon.com/Calculus-Trans.../dp/0538497904


    the full question says

    f(x)=3+x+e^x and then asks what f^-1(4) is

    NOTE: by f^-1(4) I mean 'the inverse function of f at 4'
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    Re: how to factor a polynomial to the yth degree

    Quote Originally Posted by kingsolomonsgrave View Post
    the full question says
    f(x)=3+x+e^x and then asks what f^-1(4) is
    Looking at the derivative, it easy to see that function is one-to-one.
    So f(0)=4 thus f^{-1}(4)=0.
    Thanks from topsquark
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    Senior Member MaxJasper's Avatar
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    Lightbulb Re: how to factor a polynomial to the yth degree

    It appears that your own solution is the best mirror image on y=x line:

    Attached Thumbnails Attached Thumbnails how to factor a polynomial to the yth degree-inverse-function.png  
    Last edited by MaxJasper; August 29th 2012 at 09:19 AM.
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    Re: how to factor a polynomial to the yth degree

    Quote Originally Posted by Plato View Post
    Looking at the derivative, it easy to see that function is one-to-one.
    So f(0)=4 thus f^{-1}(4)=0.
    Oh i see what the question was getting at now!
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