Problem Solving

Saw a solution to this question on one of the posting but still don't understand how the person arrived to this answer???

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

A. f(x) = x^
B. f(x) = x+1
C. f(x) = radical x
D. f(x) = 2/x
E. f(x) = -3x

Please elaborate on this solution....??

I am not sure about what do you mean by these choices...
A. f(x) = x^
C. f(x) = radical x

For this question, the correct answer is
E. f(x) = -3x

The best way to solve is back-tracking...

D. f(x) = 2/x
f(a) = 2/a, f(b) = 2/b, f(a+b) = 2/(a+b), f(a)+f(b) = 2*(a+b)/(ab)

B. f(x) = x+1
f(a) = a+1, f(b) = b+1, f(a+b) = a+b+1, f(a)+f(b) = a+b+2

Similarly you can see the other solutions...

(a) should probably be x^2 and "radical x" probably means "root x".

Simplyjat has the right answer. Multiplication is distributive (in other words x(a+b) = xa + xb), whereas those other operations aren't.