## BMO1 2009/10 Q5 functional equation: f(x)f(y)=f(x+y)+xyf(x)f(y) = f(x + y) + xy

Find all functions f, defined on the real numbers and taking real values, which satisfy the equation f(x)f(y)=f(x+y)+xy for all real numbers x and y. I worked out f(0)=1, and f(−1)f(1)=0, but then I hit a wall. Answer Setting y=0 gives f(x)f(0)=f(x). Since f cannot be identically zero, it follows that f(0)=1. Setting x=1,y=−1 then … Read more