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Intern Joined: 17 Feb 2018
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Question Stats: 66% (00:34) correct 33% (01:11) wrong based on 9 sessions
Given $$\frac{1}{2} f(x)= f (\frac{1}{2} * x)$$, which of the following is true for all values of f(x)?

A.$$f(x)= 2x+2$$

B.$$f(x)=13x$$

C.$$f(x)=x^2$$

D.$$f(x)=x-10$$

E.$$f(x)=\sqrt{(x-4)}$$

I know the answer is B and I got it by trying each f(x) function. However the answer indicates, "the fastest method is to use logical: since the order of operations says that order does not matter with multiplication and division but does matter between multiplication and addition/subtraction, or multiplication and exponents, choose a function that has only multiplication and/or division."

Could anyone explain this logic? Thank you.
[Reveal] Spoiler: OA

Last edited by Carcass on 19 Feb 2018, 02:13, edited 2 times in total.
Edited by Carcass
Intern Joined: 17 Feb 2018
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Re: A question on functions and formulas from Manhattan Prep 5lb [#permalink]
alihong2010 wrote:
Given 1/2f(x)=f(x/2), which of the following is true for all values of f(x)?

A.f(x)=2x+2
B.f(x)=13x
C.f(x)=x^2
D.f(x)=x-10
E.f(x)=sqrt(x-4)

I know the answer is B and I got it by trying each f(x) function. However the answer indicates, "the fastest method is to use logical: since the order of operations says that order does not matter with multiplication and division but does matter between multiplication and addition/subtraction, or multiplication and exponents, choose a function that has only multiplication and/or division."

Could anyone explain this logic? Thank you.

well, since the problem features transformations which feature multiplication (1/2*f(x)) and division (x/2), it's safe to say that the DM part of PEDMAS is used- I guess that leads to trying only equations with DM transformations? I'm not 100% sure either
Intern Joined: 17 Feb 2018
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Re: A question on functions and formulas from Manhattan Prep 5lb [#permalink]
alihong2010 wrote:
Given 1/2f(x)=f(x/2), which of the following is true for all values of f(x)?

A.f(x)=2x+2
B.f(x)=13x
C.f(x)=x^2
D.f(x)=x-10
E.f(x)=sqrt(x-4)

I know the answer is B and I got it by trying each f(x) function. However the answer indicates, "the fastest method is to use logical: since the order of operations says that order does not matter with multiplication and division but does matter between multiplication and addition/subtraction, or multiplication and exponents, choose a function that has only multiplication and/or division."

Could anyone explain this logic? Thank you.

What page in the book was this featured, if you don't mind me asking?
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Re: Given 1/2f(x)=f(x/2), [#permalink]
Expert's post
OE

Quote:
The fastest method is to use logic: since the order of operations says that order does not matter with multiplication and division but does matter between multiplication and addition/subtraction, or multiplication and exponents, choose a function that has only multiplication and/or division. Only answer choice (B) qualifies.

Hope this helps.
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Re: Given 1/2f(x)=f(x/2), [#permalink]
1
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Expert's post
Plugging might be a safe option if you are not familiar with polynomials.

The logical way mentioned here is:

given $$f(cx)=cf(x)$$ where $$f(x)$$ is a polynomial say $$f(x)= a_nx^n + a_{n-1}x^{n-1}.....+ a_1x + a_0$$

So $$f(cx)=a_n(cx)^n + a_{n-1}(cx)^{n-1}.....+ a_1cx + a_0$$

Here $$f(cx)=cf(x)$$ if all coeffecients except $$a_1$$ is 0 i.e a linear function or all coeffecients excepts $$a_0$$ is 0 i.e. a constant function.

Since the options have only one linear function we can safely say that is the correct answer.
_________________

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Try our free Online GRE Test Re: Given 1/2f(x)=f(x/2),   [#permalink] 19 Feb 2018, 12:08
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