Results 1 to 3 of 3

Math Help - find all functions

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    4

    find all functions

    find all functions such that : for every x ,y in R
    f(x)+f(y)=f(x+f(y))
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    Quote Originally Posted by bgbgbgbg View Post
    find all functions such that : for every x ,y in R
    f(x)+f(y)=f(x+f(y))
    Interesting question. Is there any context? For example are these linear functions? Or all functions?

    f_n(x) = x+n would be one, for all n \in \mathbb{R} (this includes the identity function), as would the zero function, f(x)=0.

    Now, if the question was about linear bijections then there is only one such function, which would be a nice question. However, this question is much too vague. I mean, the function,

    g_n(x) = \left\{<br />
     \begin{array}{lr}<br />
       x & : x \in \mathbb{Q}\\<br />
       x+n & : x \notin \mathbb{Q}<br />
     \end{array}<br />
   \right.

    is a function of this form. And it's hideous.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Oct 2009
    Posts
    769

    This is an interesting problem

    I'm posting to track the progress on this problem.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. If m<n, find # of onto functions from A onto B
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: December 2nd 2011, 06:06 PM
  2. find the functions f and g such that
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 18th 2010, 10:00 PM
  3. Find Functions f and g
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 8th 2008, 09:11 PM
  4. Log Functions...Find a
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 3rd 2008, 04:51 AM
  5. Find Functions f and g
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: January 21st 2007, 04:45 AM

Search Tags


/mathhelpforum @mathhelpforum