Question 4
Determine all functions $f:\mathbb R\to\mathbb R$ such that
$$f(x^2-y^2)=xf(x)-yf(y)$$
for every pair of real numbers $x,y$.
$$f(x^2-y^2)=xf(x)-yf(y)$$
for every pair of real numbers $x,y$.
USAMO 2002 — Days 1 and 2 Question 4
USAMO · USAMO 2002 — Days 1 and 2