Results 1 to 2 of 2

Math Help - Invertible function problem

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Invertible function problem

    Q: Suppose that the function g: R->R is continuous and that g(x) > 0 for all x in R. Define h:R->R by int (upper limit = x, lower = 0) 1/g(t). Note that h is strictly increasing on R, hence h is invertible. Set J = rang h and let f:J->R be inverse of h.

    Prove that f satisfies the differential equation:

    f'(x) = g(f(x), for all x in J
    f(0) = 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,797
    Thanks
    1690
    Awards
    1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Check whether function is invertible...?
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 22nd 2009, 07:40 AM
  2. Help on invertible function question
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 14th 2008, 02:45 PM
  3. invertible increasing function
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: August 18th 2008, 06:13 AM
  4. invertible function by graphs
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 5th 2007, 06:43 AM
  5. derivative of an invertible function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 17th 2006, 06:18 AM

Search Tags


/mathhelpforum @mathhelpforum