Results 1 to 2 of 2

Math Help - Commutativity of Inverse Functions.

  1. #1
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9

    Commutativity of Inverse Functions.

    Let, f(x) be a real valued function definited for all reals. Proof (or disproof) that is there exists a function such as g(f(x))=x is true for all reals. Then, f(g(x))=x is always true.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ThePerfectHacker
    Let, f(x) be a real valued function definited for all reals. Proof (or disproof) that is there exists a function such as g(f(x))=x is true for all reals. Then, f(g(x))=x is always true.
    Let f(x) be a sigmoid function something like the cumulative
    normal functiom, then \mathbb{R} is mapped one one onto
    (0,1), and so there is an inverse function g(y) from
    (0,1) onto \mathbb{R}

    Then f(g(x))=x holds for all x \in (0,1) but not for all x \in \mathbb{R}

    That is the domains of f\circ g and g \circ f are not equal.

    RonL
    Last edited by CaptainBlack; March 10th 2006 at 03:49 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ring Automorphisms and Commutativity
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 2nd 2011, 04:40 PM
  2. commutativity of a group
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: January 29th 2010, 08:32 AM
  3. Matrices and multiplication commutativity
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 24th 2008, 11:33 PM
  4. matrix multiplication commutativity
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: March 30th 2008, 02:13 AM
  5. Commutativity of Addition
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: July 8th 2007, 06:36 PM

Search Tags


/mathhelpforum @mathhelpforum