Question 8
(BUL 2) Find all functions $f$ defined for all $x$ that satisfy the condition
$$xf(y)+yf(x)=(x+y)f(x)f(y),$$
for all $x$ and $y$. Prove that exactly two of them are continuous.
$$xf(y)+yf(x)=(x+y)f(x)f(y),$$
for all $x$ and $y$. Prove that exactly two of them are continuous.