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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 29% (01:42) correct 71% (02:10) wrong based on 35 sessions

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[GMAT math practice question]

When $$f(x)=\frac{x^3+1}{x^3}$$, which of the following is equal to $$f(\frac{-1}{x})$$?

$$A. f(x)$$
$$B. -f(x)$$
$$C. \frac{1}{f(x)}$$
$$D. 1-f(x)$$
$$E. (f(x))^3$$

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Joined: 12 Sep 2015
Posts: 4009
When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

When $$f(x)=\frac{x^3+1}{x^3}$$, which of the following is equal to $$f(\frac{-1}{x})$$?

$$A. f(x)$$
$$B. -f(x)$$
$$C. \frac{1}{f(x)}$$
$$D. 1-f(x)$$
$$E. (f(x))^3$$

GIVEN: f(x)=(x³ + 1)/x³
So, f(-1/x) = [(-1/x)³ + 1]/(-1/x
= (-1/x³ + 1)/(-1/x³)
= (-1/x³)/(-1/x³) + (1)/(-1/x³)
= 1 - x³

Hmmm, am I missing something?

Cheers,
Brent
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Concentration: Sustainability, Marketing
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Re: When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

When $$f(x)=\frac{x^3+1}{x^3}$$, which of the following is equal to $$f(\frac{-1}{x})$$?

$$A. f(x)$$
$$B. -f(x)$$
$$C. \frac{1}{f(x)}$$
$$D. 1-f(x)$$
$$E. (f(x))^3$$

solving for $$f(\frac{-1}{x})$$
will give = (1-x^3)

I am not sure how B is coming out correct as $$-f(x)$$ = 1-x^3/ x^3
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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=>

$$f(\frac{-1}{x}) = (\frac{-1}{x})^3 + 1/{1/(\frac{-1}{x})^3} = \frac{-1}{x^3} – x^3 = -(x^3+\frac{1}{x^3}) = -f(x).$$

Therefore, B is the answer.
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GMAT 1: 640 Q44 V35 Re: When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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let x be 1
f(1) = 1+1 \ 1 = 2
f(-1/x) =f(-1) = 0
can't find any correct answer !
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Manager  G
Joined: 21 Feb 2019
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Location: Italy
Re: When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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MathRevolution wrote:
=>

$$f(\frac{-1}{x}) = (\frac{-1}{x})^3 + 1/{1/(\frac{-1}{x})^3} = \frac{-1}{x^3} – x^3 = -(x^3+\frac{1}{x^3}) = -f(x).$$

Therefore, B is the answer.

I still don't understand. Shouldn't it be, in the first passage, $$(\frac{-1}{x})^3 + 1/{(\frac{-1}{x})^3}$$?
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MEMENTO AUDERE SEMPER
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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lucajava wrote:
MathRevolution wrote:
=>

$$f(\frac{-1}{x}) = (\frac{-1}{x})^3 + 1/{1/(\frac{-1}{x})^3} = \frac{-1}{x^3} – x^3 = -(x^3+\frac{1}{x^3}) = -f(x).$$

Therefore, B is the answer.

I still don't understand. Shouldn't it be, in the first passage, $$(\frac{-1}{x})^3 + 1/{(\frac{-1}{x})^3}$$?

We plugged in $$-\frac{1}{x}$$ for x.
_________________ Re: When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?   [#permalink] 31 Mar 2019, 13:27
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