Thread: Function finding

1. 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?

2. Re: Function finding

Where from do you know that $f(x)=0 ,and ,f(y)=0$ are all function that satisfy this equation?

3. 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...

4. Re: Function finding

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?
Asked here: http://www.mathhelpforum.com/math-he...on-188990.html

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