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

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

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New post Updated on: 25 Sep 2014, 23:41
3
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00:00
A
B
C
D
E

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  35% (medium)

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.
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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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New post 25 Sep 2014, 21:43
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\(f(x) = \frac{x^4 - 1}{x^2} = x^2 - \frac{1}{x^2}\)

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

Answer = B
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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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New post 19 Nov 2007, 10:23
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)

Answer is B.
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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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New post 25 Sep 2014, 23:41
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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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New post 11 Jul 2015, 00:15
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 :-D

After solving the function the result is (1-x^4)/x^2
so, B is the perfect explanation
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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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New post 18 Jul 2017, 22:19
I listed some examples at the bottom for anyone struggling with these types of questions.

https://www.youtube.com/watch?v=T6-Zdr5w_bE
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Function question 22.png
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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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New post 04 Feb 2019, 22:24
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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Re: If f(x) = (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?  [#permalink]

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New post 04 Feb 2019, 22:38
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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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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