easy one:)
f(a+b) should be equal to f(a) + f(b)

now, its only possible when f(x)=-3x


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

add the two

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

is it clear now?

not really... could u pls give more details?

Pls let me know How you arrived at A?

shibal wrote:not really... could u pls give more details?

i justed guessed.... had no idea how to work the problem out...

Substitute #'s, say a=2 and b=4.

For example for the first one:
(2+4)^2 and 2^2 +4^2.
The two equations are not equal.
Only E satisfies the requirement.

i'm sorry, but i can't see how to do this one....

You have to plug in (a + b) in place of x and see if both the sides match.

Lets take A - f(x) = x^2

x = (a + b), x = a, x = b

L.H.S - f(a + b) = (a + b)^2
R.H.S - f(a) + f(b) = a^2 + b^2

therefore L.H.S is not equal to R.H.S

follow the same thing for rest of the answer choices and you'll get the right answer.

shibal wrote:i'm sorry, but i can't see how to do this one....

I think, we can go to correct option by doing trail and error by substituting some values and check it..

E option will be the only correct option if one goes by that way.