The approach I would take is to plug in a+b in place of x into each function (this is f(a+b)) then see if you can rearrange to get something equal to f(a)+f(b).

A. f(a+b) = (a+b)^2 = a^2 + 2ab + b^2 = f(a)+f(b)+2ab
B. f(a+b) = a + b + 1 = f(b) + a
C. f(a+b) = sqrt(a+b) not equal f(a)+f(b) = sqrt(a)+sqrt(b)
D. f(a+b) = 2/(a+b) not equal f(a)+f(b) = 2/a + 2/b
E. f(a+b) = -3(a+b) = -3a+-3b = f(a)+f(b)

Thanks a lot! It was very helpful.