Functions question from GMATclub m25 : PS Archive
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# Functions question from GMATclub m25

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Manager
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Functions question from GMATclub m25 [#permalink]

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29 Sep 2009, 08:12
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Guys, need your help on understanding this one - comes from GMAT Club test m25 Q22. Have not found it via search. Would love to get a thorough explanation. Thanks!

If function f(x) satisfies $$f(x)=f(x^2)$$ for all x, which of the following must be true?

A. f(4)=f(2)f(2)
B. f(16)-f(-2)=0
C. f(-2)+f(4)=0
D. f(3)=3f(3)
E. f(0)=0

The OA is here
[Reveal] Spoiler:
B. f(-2)=f(2)=f(4)=f(16). The other choices are not necessarily true. Consider f(x)=3 for all x.
Manager
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Re: Functions question from GMATclub m25 [#permalink]

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29 Sep 2009, 08:32
f(2) = f(4) = f(16)

so option B is correct
Manager
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Re: Functions question from GMATclub m25 [#permalink]

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29 Sep 2009, 08:58
I know the answer, thank you

What I need is the logic behind it and why the other options are not correct.
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Re: Functions question from GMATclub m25 [#permalink]

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29 Sep 2009, 09:15
Well at first go, even i had no idea, just trying to understand.
Everything is defined in term of functions, and function can be defined in any way
like it can be
f(X) = ax+b or \sqrt{x}, so its only become true for B, its kind of weird that, in B we are keep on substituting for second function and keeping first part as it is, i think it can be only B which can equate to RHS and no other option is possible/true.
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Re: Functions question from GMATclub m25 [#permalink]

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29 Sep 2009, 09:19
even E looks true, but remember its a function in general. so it cannot be true. Only B, once you substitute F(16) for F(-2) ; F(16) - F(16) = 0
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Re: Functions question from GMATclub m25 [#permalink]

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29 Sep 2009, 09:55
manojgmat wrote:
even E looks true, but remember its a function in general. so it cannot be true.

Thanks for trying to explain! What did you mean by the above? I actually picked this answer as it seemed less complicated to me.

This is the question where I get quite lost so far...
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Re: Functions question from GMATclub m25 [#permalink]

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29 Sep 2009, 11:07
Just forget it, incase u have not picked E too..
Manager
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Re: Functions question from GMATclub m25 [#permalink]

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29 Sep 2009, 12:21
That's exactly what I picked although did look a bit suspicious
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Re: Functions question from GMATclub m25 [#permalink]

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23 Jan 2010, 00:25
i'm totally lost on this one. could someone please explain the solution to this question?
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Re: Functions question from GMATclub m25 [#permalink]

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23 Jan 2010, 10:10
b)f(16)-f(-2)=0

if the ans is b by substituting f(-2)=f(4)=f(16)

u can also have f(16)=f(256) and so on..

the question asks which ans choice is correct for all x

I am still not convinced there must be some better expalantion

Last edited by silasaaa2 on 23 Jan 2010, 10:11, edited 1 time in total.
Manager
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Re: Functions question from GMATclub m25 [#permalink]

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23 Jan 2010, 10:10
but i am against choice E as well as the question says for all x.

choice E will hold gold only if x is zero not for other values of x
Re: Functions question from GMATclub m25   [#permalink] 23 Jan 2010, 10:10
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