EIVs - Formulas Question

[tsuttonc]

GMATPrep Software Practice Test Question...

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

The answer is E, but I'm not sure why and the GMATPrep Software doesn't give an explanation. Could someone please help me me understand? Thanks!

[mxs2009]

Because this is a problem solving question, and the stem states, "for all positive numbers a and b," I would just pick numbers. a=1 b=3

A. f(1+3) = f(1)+f(3)
4^2 = 1^2 + 3^2
16=2+9 => NO
B. (4+1) = (1+1) + (3+1)
5=2+4 => NO
C. √4 = √1 + √3
2=1+√3 => NO
D. 2/4 = 2/1 + 2/3
1/2 = 8/3 => NO
E. -3(4) = -3(1) + -3(3)
-12 = -12 => YES

[RonPurewal]

for-which-of-the-following-functions-is-f-a-b-f-a-f-b-t2795.html