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

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Manager
Joined: 05 May 2005
Posts: 78
For which of the following functions f(a+b) = f(a) + f(b) [#permalink]

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11 Dec 2008, 10:18
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Here is a function problem from GMATPrep, Practice Test 1:

For which of the following functions 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

d) f(x) = 2/x

e) f(x) = -3x
Intern
Joined: 05 Dec 2008
Posts: 20

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12 Dec 2008, 21:55
above720 wrote:
Here is a function problem from GMATPrep, Practice Test 1:

For which of the following functions 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

d) f(x) = 2/x

e) f(x) = -3x

This is one of those awful questions where you have to try every answer choice.
HOWEVER, when the only way to get the answer is to try every answer choice, ALWAYS start from E and work up.
More often than not the answer appears near the bottom and the test writers want you to waste time.

E) --> Is it the case that f(a+b) = f(a) + f(b)?
One method is to plug in numbers for a and b. Another method is to look at it algrbraically.

For this function we get the proposed equation -3(a+b) = -3(a) + -3(b) Does this equation always hold true? Yep.

Just to show what this question is about (since many people find function notation difficult) let's try A as well.
For this function we get the proposed equation (a+b)^2 = -a^2 + b^2 Does this equation always hold true? Nope. (try a few values for a and b)

For this function we get the proposed equation (a+b)+1= a+1 + b+1 Does this equation always hold true? Nope. (try a few values for a and b)

And so on . . .
Re: Function Problem f(a+b)   [#permalink] 12 Dec 2008, 21:55
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# For which of the following functions f(a+b) = f(a) + f(b)

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