请教：GMATPrep math 一道

mbz

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

a. f(x) = x^2

b. f(x) = x + 1

c. f(x) = square root x

d. f(x) = 2/x

e. f(x) = -3x

The answer is e,   but I have no clue. 

Could someone please explain it?

mbz

I just figured it out myself.

Thanks everyone.

kennycatter

一个个代落，比如第一个：f(a) +f(b)=a^2+b^2,而f(a+b)=(a+b)^2,显然不相等。还可以通过f(0)=0来判断。

直接看的话就看感觉了，f(a+b) = f(a) +f(b) 感觉就像分配律，再比如f(a+b) = f(a) *f(b)，就是次方,比如2^x。