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For which of the following functions is f(a+b) = f(a) + f(b)

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Intern
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For which of the following functions is f(a+b) = f(a) + f(b) [#permalink] New post 31 Aug 2007, 09:20
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) = x^(1/2)
d) f(x) = 2/x
e) f(x) = -3x

*It would be greatly appreciated if you could provide step-by-step approach to solving this one
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Re: Functions - GMATPrep [#permalink] New post 31 Aug 2007, 09:37
jp888 wrote:
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) = x^(1/2)
d) f(x) = 2/x
e) f(x) = -3x

*It would be greatly appreciated if you could provide step-by-step approach to solving this one


E

Pick a number, then plug in
Set x = 3 = 1+2

f(3):f(1):f(2):f(1)+f(2)

A) 9:1:4:5
B) 4:2:3:5
C) sqrt(3):1:sqrt(2):sqrt(2)+1
D) 2/3:2:1:3
E) -9:-3:-6:-9

E is correct.
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 [#permalink] New post 01 Sep 2007, 03:46
E

f(x) = -3x
f(y) = - 3x
f(x) + f(y) = -3x - 3y

f(x+y) = -3(x+y) = -3x - 3y

So f(x)+f(y) = f(x+y)
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Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
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Re: Functions - GMATPrep [#permalink] New post 02 Jul 2011, 23:36
i dont think so i understood why the answer is to be E

the question says that the function given in the 1st line is only for positive numbers and all the 4 options work for that...but it has clearly said that it wont work for negative numbers, hence E should be the one?

Can someone please explain the reasons for choosing E as the answer...
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Re: Functions - GMATPrep   [#permalink] 02 Jul 2011, 23:36
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For which of the following functions is f(a+b) = f(a) + f(b)

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