
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 9th, 2019, 06:22 AM  #1 
Newbie Joined: Mar 2019 From: USA Posts: 4 Thanks: 0  Need help with a functional equation
$$ f: \mathbb{R} \to \mathbb{R}\qquad \frac{f(x+y)}{x+y} = \frac{f(x)f(y)}{xy}, \qquad \forall x,y\in \mathbb{R}, \leftx\right \neq \lefty\right $$ Can I prove anything interesting about this function? I need to find it. 
March 9th, 2019, 06:47 AM  #2 
Senior Member Joined: Oct 2009 Posts: 864 Thanks: 328 
Start by filling in some interesting values. For exampe x=0, y=1, ...

March 9th, 2019, 07:22 AM  #3 
Newbie Joined: Mar 2019 From: USA Posts: 4 Thanks: 0 
I’ve already tried.. the only thing that results is f(0)=0

March 9th, 2019, 12:29 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,823 Thanks: 723 
f(2x)=2xf'(x). Interesting?


Tags 
ecuation, equation, functional 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Functional equation  idontknow  Elementary Math  2  March 22nd, 2018 12:31 PM 
Functional Equation  desum  Elementary Math  0  May 10th, 2012 04:03 AM 
Functional equation  arnold  Algebra  1  October 13th, 2011 04:23 AM 
Functional equation  georgij  Algebra  3  October 9th, 2011 02:55 AM 
can you help me is a functional equation  llambi  Math Events  4  April 22nd, 2011 05:57 AM 