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# When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?

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Math Revolution GMAT Instructor
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When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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25 Mar 2019, 00:31
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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend Joined: 12 Sep 2015 Posts: 4009 Location: Canada When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)? [#permalink] ### Show Tags 25 Mar 2019, 06:59 1 Top Contributor 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 _________________ Test confidently with gmatprepnow.com GMAT Club Legend Joined: 18 Aug 2017 Posts: 5020 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)? [#permalink] ### Show Tags 25 Mar 2019, 09:01 1 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 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] ### Show Tags 27 Mar 2019, 01:01 => $$f(\frac{-1}{x}) = (\frac{-1}{x})^3 + 1/{1/(\frac{-1}{x})^3} = \frac{-1}{x^3} – x^3 = -(x^3+\frac{1}{x^3}) = -f(x).$$ Therefore, B is the answer. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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29 Mar 2019, 04:23
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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Re: When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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29 Mar 2019, 06:33
1
MathRevolution wrote:
=>

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

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

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31 Mar 2019, 13:27
lucajava wrote:
MathRevolution wrote:
=>

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

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.
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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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