For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b ?

(A) f(x) = x 2

(B) f(x) = x + 1

(C) f(x) = √x

(D) f(x) = 2/x

(E) f(x) = -3x

没看懂题目，完全没思路。。。

这道题目其实很基本阿 简单说就是在考察函数的线性性质

一个比较简单的办法就是随便找几个数字算算

取a=2 b=1

那么满足  f(a + b) = f(a) + f(b) 意味着  f(2 + 1) =f(3)= f(2) + f(1)

A f(3) = 3^2 = 9 但是 f(2)+f(1)= 2^2 + 1^2 = 4+1 = 5 不满足

B f(3) = 3+1 = 4 但是 f(2)+f(1)= 2+1 + 1+1 = 3+2 = 5 不满足

C f(3) = √3  但是 f(2)+f(1)= √2 + √1 = √2+1  不满足

D f(3) = 2/3  但是 f(2)+f(1)= 2/2+2/1 = 1+2 = 3 不满足

E f(3) = -3*3 = -9  而 f(2)+f(1)= -3*2 + -3*1 = -6 + -3 = -9 满足