# Function finding

• October 4th 2011, 07:43 AM
GGPaltrow
Function finding
To determine all the functions $f$ defined on the set of real numbers and obtaining real values such that for any real numbers $x, y$ such equation is true:
$f(x+f(x+y))-f(x-y)-f(x)^2=0$

It works supposing $f(x)=0 and f(y)=0$ but I'm clueless on the next step. Could you please help?
• October 4th 2011, 10:49 AM
geagry
Re: Function finding
Where from do you know that $f(x)=0 ,and ,f(y)=0$ are all function that satisfy this equation?
• October 5th 2011, 04:11 AM
GGPaltrow
Re: Function finding
I don't. It was just an example set of correct data. As I stated, I don't know how to acquire the other ones...
• October 18th 2011, 03:36 AM
mr fantastic
Re: Function finding
Quote:

Originally Posted by GGPaltrow
To determine all the functions $f$ defined on the set of real numbers and obtaining real values such that for any real numbers $x, y$ such equation is true:
$f(x+f(x+y))-f(x-y)-f(x)^2=0$

It works supposing $f(x)=0 and f(y)=0$ but I'm clueless on the next step. Could you please help?