I think the answer should be E.

If i am correct let me know..so that i can shoot my logic..

why is it E?

I don't even know where to start with this question.

Another vote for e.

I find just plugging in numbers to something like this the most intuitive.

let a=1, and b=2

then, go through the answer choices and plug it in:
so if
f(x) = -3x (answer choice e)

then,
f(a) = f(1) = -3(1) = -3
f(b) = f(2) = -3(2) = -6
f(a+b) = f(1+2) = f(3) = -3(3) = -9

thus
f(a+b) = f(a) + f(b)

If you try this out on other answer choices, you'll see that it doesn't fit.