This can be solved by simply checking with all answer choices,=.

a) f(x)= x^2

f(a+b)=(a+b)^2=a^2+b^2+2ab
f(a)+f(b) = a^2+b^2

So, a is not the answer

b) f(x) = x+1

f(a+b)=a+b+1
f(a)+f(b) = a+1+b+1 = a+b+2

So, b is not the answer

c) f(x)= root(x)
Since root(a+b) <> root(a) + root(b)

So, c is not the answer

d) 2/(a+b) <> 2/a + 2/b

So, d is not the answer

e) -3(a+b) = -3a-3b
This will be equal for all values of a and b

Hence E is the answer.

Nothing in question says that A and B will be different positive numbers, so

A=B=1

In other words

Look for f(2) = 2f(1)

very easy calculations. ..> E

TIP: when you plug numbers start from the bottom!

think about it this way..
Just replace x with a, b and a+b

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

f(x) = -3x

1. f(a+b) = -3(a+b)

2. f(a) = -3(a)

3 f(b) = -3(b)

for other options LHS and RHS will not match