# Function finding

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

It works supposing \$\displaystyle f(x)=0\$ and \$f(y)=0\$ but I'm clueless on the next step. Could you please help?
• Oct 4th 2011, 10:49 AM
geagry
Re: Function finding
Where from do you know that \$\displaystyle f(x)=0 ,and ,f(y)=0\$ are all function that satisfy this equation?
• Oct 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...
• Oct 18th 2011, 03:36 AM
mr fantastic
Re: Function finding
Quote:

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

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