MEMO 2009 pojedinačno problem 1
Dodao/la:
arhiva28. travnja 2012. Find all functions
![f: \mathbb{R} \to \mathbb{R}](/media/m/6/0/2/60240831e50878f32015939a09239ca6.png)
, such that
![f(xf(y)) + f(f(x) + f(y)) = yf(x) + f(x + f(y))](/media/m/7/4/5/74505d12eeab72ed7454ec1db5c2c13e.png)
holds for all
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
,
![y \in \mathbb{R}](/media/m/7/8/c/78c6bd0dd1e2faa59dcb4d67decaef9f.png)
, where
![\mathbb{R}](/media/m/1/4/0/140a3cd0f5aa77f0f229f3ae2e64c0a6.png)
denotes the set of real numbers.
%V0
Find all functions $f: \mathbb{R} \to \mathbb{R}$, such that $$f(xf(y)) + f(f(x) + f(y)) = yf(x) + f(x + f(y))$$ holds for all $x$, $y \in \mathbb{R}$, where $\mathbb{R}$ denotes the set of real numbers.
Izvor: Srednjoeuropska matematička olimpijada 2009, pojedinačno natjecanje, problem 1