Function

[Marisa]

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

a) f(x)=x^2
b) f(x)=x+1
c) f(x)=sqrtx
d) f(x)=2x
e) f(x)= -3x

[vcgmat]

answer (E)

[Marisa]

Thank you. I know the answer, how did you come to that conclusion?

[vcgmat]

Let a = 1 and b=2

1. Case#1 - f(x) = x^2
f(a+b) = f(3) = 9
f(1) + f(2) = 1 + 4 = 5
so f(a+b) <> f(a) + f(b)
try similar logic for other answer choices.

(E) the condition becomes equal

[devesh99]

Hi Vcgmat

F(a+b) = f(a) + f(b) holds good for both option D & E..

Can you explain .. how did u get to E as the answer..

[devesh99]

Hi Vcgmat

F(a+b) = f(a) + f(b) holds good for both option D & E..

Can you explain .. how did u get to E as the answer..

[naaga]

anyone can explain in detail.....still I didn't understand the procedure ....thanks in advance..

[franciskyle]

I have seen this question before, and I think that D should actually be 2/3 not 2x. That would make it possible to solve.

All you need to do for this one is plug A+B, A & B into each respective equation to see if they equate.

A:

(A+B)^2 NOT= A^2 + B^2

B:

(A + B) + 1 NOT= (A+1) + (A+1)

C:

sqrt(A+B) NOT= sqrt(A) + sqrt(B)

D:

2/3 NOT= 2/3 + 2/3

E:

-3(A+B) = -3A + -3B

[franciskyle]

Ps: The answer is E, because the two sides of the equation are equal.

[avenus]

f(a+b) = f(a)+f(b)

every linear function complies with this (also with f(ka) = k f(a), where k is a constant)

Both d) and e) are linear functions so, clearly, both are correct answers

If this is a real GMAT question, guess there must be some sort of typo...