Substitute (a+b) in place of x in each of the following functions and then try try to express it term of f(a) and f(b) and see if it is equal to f(a)+f(b)
for example
(a) f(x)=x^2
Substituting (a+b) in place of x gives f(a+b)= (a+b)^2 = (a^2) + (b^2) +2a*b = f(a) + f(b) +2*a*b --------- (hence not a correct option)
similarly
(b) f(x)=x+1
After substitution f(a+b) = a+b+1 = (a+1) + (b+1) -1 = f(a)+f(b) -1 ----------- (Hence again not a correct option)
(c) rootunder x
After substitution f(a+b)= rootunder(a+b) which is not equal to rootunder(a) +rootunder(b) ----------- (Hence again not a correct option)
(d) f(x)=x/2
After substitution f(a+b)= (a+b)/2 = (a/2) + (b/2) = f(a) + f(b) ----------Hence the correct answer
(e) f(x)=-3x
After substitution f(a+b)= -3(a+b) = -3a -3b = (-3a) + (-3b) = f(a) + f(b) ---------- Again correct answer
