$ P(0,0,0)$ implies $ f(0)=0$. We can compare $ P(x,y,z)$ and $ P(0,x+y,z)$ and get $ f(2\sqrt{xz})+f(2\sqrt{yz})=f(2\sqrt{xz+yz})$ for $ x+y\ge z$. It is not hard to prove $ f(\sqrt{x})+f(\sqrt{y})=f(\sqrt{x+y})$ for $ x,y\ge0$ $ g(x)=f(\sqrt{x})$ has cauchy equation and is increasing. So $ f(x)=g(x^2)=cx^2$, where $ c>0$

hi, in this function if I get $f(z-x)=f(x-z)$, what it means??

arshakus wrote: hi, in this function if I get $f(z-x)=f(x-z)$, what it means?? It means the function is even.