For all the positive integers, f(ab)=f(a)f(b), which of the : PS Archive
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# For all the positive integers, f(ab)=f(a)f(b), which of the

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For all the positive integers, f(ab)=f(a)f(b), which of the [#permalink]

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31 Jan 2005, 10:15
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For all the positive integers, f(ab)=f(a)f(b), which of the following must be true?
1. f(x)=x^(1/2) 2. f(x)=3x 3. f(x)= -x
VP
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31 Jan 2005, 10:39
My guess will be "2" i.e. f(x)=3x. Altho I have to admit I don't understand the problem correctly.
Reason I chose 2 is because the ques is about postive integers and not abt fractions and -ve integers.
SVP
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31 Jan 2005, 11:18
Answer should be (I), but the question is not correctlyn worded.

(I)f(x)=x^(1/2)
f(a)=a^1/2
f(b)=b^1/2
f(ab)=(AB)^1/2
=>f(ab)=f(a)f(b)

(II)f(x)=3x
f(a)=3a
f(b)=3b
f(a)f(b)=9ab
f(ab)=3ab<>f(a)f(b)

You can do the same thing for (III) and find they are not eqaul either.
Director
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31 Jan 2005, 11:24
i still do not understand the question fully..
VP
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31 Jan 2005, 11:36
I get it now....agree with Hong....now I am clear on what the ques is abt.
VP
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31 Jan 2005, 13:06
HongHu wrote:
Answer should be (I), but the question is not correctlyn worded.

(I)f(x)=x^(1/2)
f(a)=a^1/2
f(b)=b^1/2
f(ab)=(AB)^1/2
=>f(ab)=f(a)f(b)

(II)f(x)=3x
f(a)=3a
f(b)=3b
f(a)f(b)=9ab
f(ab)=3ab<>f(a)f(b)

You can do the same thing for (III) and find they are not eqaul either.

gr8 Hong,
you have pretty clear concept.........
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31 Jan 2005, 15:44
Does anyone know if this is how poorly worded some of the actual GMAT questions are?
31 Jan 2005, 15:44
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