已知函数f(x)对任意的实数x,y都有:f(x+y)=f(x)+f(y),且f(2)=4,则f(-1)等于多少

是-2
f(0) = f(0) + f(0) => f(0) = 0
f(2) = f(1) + f(1) = 4 => f(1) = 2
f(0) = f(1) + f(-1) => f(-1) = -2
之所以自变量取相反数函数值就为相反数,是因为“对任意的实数x,y都有:f(x + y) = f(x) + f(y)”这个限制条件决定的
其实从f(x + y) = f(x) + f(y)可以推导出f(x) = kx ,其中k = f(1),它就是个正比例函数,当然自变量取相反数函数值就一定互为相反数啦,具体的推导过程很简单,但是很难想到：就是一步步论证对任意k都有f(kx) = kf(x),那么f(x) = f(x * 1) = xf(1),证明就结束了