f(0 + 1) = f(0) + f(1)
f(1) = f(0) + f(1)
f(0) = 0
令 y = -x ,则
f(x - x)= f(x) + f(-x)
f(0) = f(x) + f(-x)
0 = f(x) + f(-x)
f(-x) = -f(x)
所以该函数为奇函数