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SVP  Joined: 21 Jan 2007
Posts: 2253
Location: New York City
If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?  [#permalink]

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Question Stats: 70% (01:27) correct 30% (01:59) wrong based on 399 sessions

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If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?

A. f(x)
B. -f(x)
C. 1/f(x)
D. -1/f(x)
E. 2*f(x)

Originally posted by bmwhype2 on 19 Nov 2007, 10:02.
Last edited by Bunuel on 25 Sep 2014, 23:41, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
SVP  Status: The Best Or Nothing
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Re: If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?  [#permalink]

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$$f(x) = \frac{x^4 - 1}{x^2} = x^2 - \frac{1}{x^2}$$

$$f(\frac{1}{x}) = \frac{1}{x^2} - x^2 = -f(x)$$

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Manager  Joined: 25 Jul 2007
Posts: 91
Re: If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?  [#permalink]

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f(1/x) = ((1/x)^4 - 1) / ((1/x)^2)
= ((1/x^4) - 1) / (1/x^2)
= ((1-x^4)/(x^4)) / (1/x^2)
= (1-x^4)/(x^2)
= - ( (x^4) -1) / (x^2)
= -f(x)

Math Expert V
Joined: 02 Sep 2009
Posts: 58421
Re: If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?  [#permalink]

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bmwhype2 wrote:
If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?

A. f(x)
B. -f(x)
C. 1/f(x)
D. -1/f(x)
E. 2*f(x)

Check other Functions questions in our Special Questions Directory.
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GPA: 3.35
Re: If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?  [#permalink]

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bmwhype2 wrote:
If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?

A. f(x)
B. -f(x)
C. 1/f(x)
D. -1/f(x)
E. 2*f(x)

Answer is B After solving the function the result is (1-x^4)/x^2
so, B is the perfect explanation
Manager  B
Joined: 31 Dec 2016
Posts: 65
Re: If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?  [#permalink]

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I listed some examples at the bottom for anyone struggling with these types of questions.

Attachments Function question 22.png [ 341.92 KiB | Viewed 2498 times ]

Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?  [#permalink]

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bmwhype2 wrote:
If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?

A. f(x)
B. -f(x)
C. 1/f(x)
D. -1/f(x)
E. 2*f(x)

So lets plug in

x = 2

f(x) = x^2 - 1/x^2

f(1/x) = 1/x^2 - x^2

f(2) = 4 - 1/4

f(1/2) = 1/4 - 4

f(x) =- f(x)

B
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Manager  G
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GMAT Date: 03-15-2015
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Re: If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?  [#permalink]

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You can even plug in values to find the answer
Put $$x=1$$ , then $$f(x)=f(1/x)$$
$$f(1) = 0$$, Hence C,D and E are out
Take another sample value , say 2
$$f(2) = \frac{7}{4} , f(\frac{1}{2})= -\frac{7}{4}$$
Hence B is the right option
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KUDOS will increase your score Re: If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?   [#permalink] 04 Feb 2019, 22:38
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