Results 1 to 4 of 4

Math Help - inverse function

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    Milwaukee
    Posts
    22

    inverse function

    let f^(-1) : R->R be the inverse function of f(x)= x^5+2x+2. Find (f^(-1))'(5)

    1. So im guessing i take the inverse function of x^5+2x+2? but i'm having trouble figuring it out.

    2. I think i take the derivative of the inverse function

    3. And then i think i plug in 5

    any hoo i need help to figure this out please and thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: inverse function

    Quote Originally Posted by chizmin10 View Post
    let f^(-1) : R->R be the inverse function of f(x)= x^5+2x+2. Find (f^(-1))'(5)

    1. So im guessing i take the inverse function of x^5+2x+2? but i'm having trouble figuring it out.

    2. I think i take the derivative of the inverse function

    3. And then i think i plug in 5

    any hoo i need help to figure this out please and thank you
    You will want to use the inverse function theorem.

    If we take the derivative we get f'(x)=5x^4+2

    Since this derivative is non zero the function is 1-1 and we can use the inverse function theorem.

    To do so we need to solve the equation

    5=x^5+2x+2 \iff x^5+2x-3=0

    By the rational roots theorem the only possible zeros are \pm 1, \pm 3

    Checking x=1 \implies 1^5+2(1)-3=0


    Now by the inverse function theorem we have

    \frac{d}{dx}f^{-1}(x)\bigg|_{x=5}=\frac{1}{f'(1)}=\frac{1}{5(1)^4+  2}=\frac{1}{7}
    By the rational roots theorem we
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2012
    From
    Milwaukee
    Posts
    22

    Re: inverse function

    Thank you very much, one last question why is 3 a possible zero?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: inverse function

    Quote Originally Posted by chizmin10 View Post
    Thank you very much, one last question why is 3 a possible zero?
    For any polynomial p(x)=a_nx^n+a_{n-1}x^{n-1}+....+a_1x+a_0

    The possible rational zeros are \frac{p}{q} where p and q are all the possible factors are a_n and a_0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. function composition and inverse function
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: November 10th 2009, 12:18 PM
  2. Replies: 2
    Last Post: October 19th 2009, 02:47 AM
  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