Question

定义在R上的函数f（x）满足f（x+y）=f（x）+f（y）+2xy(x,y属于R),f(1)=2,求f(-3)=

Answer 1

f(1) = f(1) + f(0) + 2 * 1 * 0
可以算出f(0)
f(2) = f(1) + f(1) + 2 * 1 * 1
可以算出f(2)
f(3) = f(2) + f(1) + 2 * 2 * 1
可以算出f(3)
f(0) = f(-3) + f(3) + 2 * 3 * -3
可以算出f(-3)

Answer 2

回答：
由f(1+1) = f(1)+f(1) +2x1x1，得f(2) = 2+2+2x1x1 = 6;
由f(2+2) = f(2)+f(2) + 2x2x2，得f(4) = 6+6+2x2x2 = 20;
由f(4-3) = f(4)+f(-3) + 2x4x(-3)，得f(-3) = f(1) - f(4) - 2x4x(-3) = 6。