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

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New post 25 Mar 2019, 00:31
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A
B
C
D
E

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  85% (hard)

Question Stats:

29% (01:42) correct 71% (02:13) wrong based on 34 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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When f(x)=x^3+1/x^3, which of the following is equal to f(-1/x)?  [#permalink]

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New post 25 Mar 2019, 06:59
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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
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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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New post 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
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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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New post 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
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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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New post 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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New post 29 Mar 2019, 06:33
1
MathRevolution wrote:
=>


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

Therefore, B is the answer.
Answer: B


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


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

Therefore, B is the answer.
Answer: B


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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