When ever a Question asks for which of the following is true, check the answer E as GMAT would love us to start at A and work our time off before arriving at E

f(x)= -3x

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

f(a) = -3a

f(b) = -3b

f(a) + f(b) = -3(a+b) = f(a+b) Hence E

Anamika,

I think your basic issue was you got this wrong so lets take each of the case and you will realise it once you subsitute.

For any function if you just replace the value in bracket with whatever its suppose replace, it becomes much simpler to solve.

In this case lets do it case by case.

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

(3^2 + 4^2 is not equal to 9 ^2) ...so this is wrong ....
Other way this says a^2 + b^2 = a^2 + b^2 + 2ab which is wrong ....

2. f(a) = a+1
f(b) = b+1
f(a+b) = (a+b) + 1
But f(a) + f(b) will give u a+b+2 ...so this is not same as f(a+b)

3. f(a) = sqrt (a)
f(b) = sqrt (b)
f(a+b) = sqrt (a+b)

say a = 9 b = 16
f(9) = 3
f(16) = 4
f(9) + f(16) = 7

but f (9+16) = f(25) = 5

4. f(a) = 2/a
f(b) = 2/b

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

f(a+b) = 2/(a+b)
again not equal

and last option you already have answer which is correct answer...