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SVP  Joined: 21 Jan 2007
Posts: 2258
Location: New York City
If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?  [#permalink]

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Question Stats: 65% (01:36) correct 35% (01:52) wrong based on 587 sessions

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If f(x) = x^2/(x^4 - 1), 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 16 Nov 2007, 08:16.
Last edited by Bunuel on 25 Sep 2014, 23:43, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Director  Joined: 09 Aug 2006
Posts: 603
Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?  [#permalink]

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

f[x]
-f[x]
1/f[x]
-1/f[x]
2*f[x]

If x = 2 then f(x) = 4/15 and f(1/x) = -4/15 which is equal to -f(x)

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

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

f[x]
-f[x]
1/f[x]
-1/f[x]
2*f[x]

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

I pick B.

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

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

f[x]
-f[x]
1/f[x]
-1/f[x]
2*f[x]

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

Clearly, the only answer that could make sense is C

what is the OA ?
Intern  Joined: 12 Feb 2007
Posts: 9
Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?  [#permalink]

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It is B f(x) = x^2/(X^4 - 1)
f(1/x) = (1/x)^2/((1/x)^4 -1)
= (1/x)^2/(-(x^4- 1)/x^4)
= x^4/x^2 * -(1- x^4)
= (x^2 * x^2)/ x^2 * -(1-x^4)
= f(x) * (x2/ -x2)
= -f(x)
SVP  Joined: 29 Mar 2007
Posts: 2003
Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?  [#permalink]

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

f[x]
-f[x]
1/f[x]
-1/f[x]
2*f[x]

(1/x^2)/(1/x^4-1) --> (1/x^2)/(1-x^4)/(x^4) --> just cancel out the x's. we get x^2/(1-x^4) --> x^2/-(x^4-1) ---> -(x^2)/(x^4-1)

so we get -f(x). So B

U can do it algebraically, which i suggest u do first, but if its not workin out for ya then just plug in a value for x. (obviously use easy numbers).

Just make X=2.

4/16-1 ---> 4/15

Then (1/4)/(1/16-1) ---> 1/4/-15/16 --> -4/15 ---> so its b b/c -(-4/15) ---> 4/15.
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Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?  [#permalink]

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

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

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

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

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

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bmwhype2 wrote:
If f(x) = x^2/(x^4 - 1), 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)

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

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GK_Gmat wrote:
bmwhype2 wrote:
f(x) = x^2 / (x^4 - 1)
What is f(1/x) in terms of f(x)?

f[x]
-f[x]
1/f[x]
-1/f[x]
2*f[x]

If x = 2 then f(x) = 4/15 and f(1/x) = -4/15 which is equal to -f(x)

how , f(1/x) = -4/15
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Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?  [#permalink]

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Can someone explain the answer to this question with the number picking technique?

For example x=2?
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?  [#permalink]

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Hi eddyki,

You can absolutely TEST VALUES on this question. Here's how:

We're given a function to work with: f(X) = (X^2)/(X^4 -1)

We're asked to consider how the f(X) and the f(1/X) relate to one another, so we have to calculate both options.

TESTING X = 2 gives us...

f(2) = (4)/(16 - 1) = 4/15

f(1/2) = [(1/2)^2]/[(1/2)^4 - 1]

= [1/4]/[1/16 - 1]
= [1/4]/[-15/16]

= [1/4][-16/15]
= -4/15

So after doing all of these little calculations, we have proof that f(X) and the f(1/X) give OPPOSITE results.

This means that f(1/X) is the NEGATIVE of f(X).

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

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$$f(x) = x^2/(x^4-1)$$ that means that$$f(1/x) = (x^4-1)/x^2$$

I dont understand the steps after this. How do you conclude from this that its -f(x)?

What are these functions called? I need to study this..
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Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?  [#permalink]

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I find easiest way just plug in x=2, then you get f(x) = 4/15 and f(1/x) = -4/15, thus answer is B
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Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?  [#permalink]

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

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My big issue with most of the people solving is they skip basically all the steps. Not really good for learning when you do that. Here is a complete solution and a good video explaining how function notation works.

Attachments Function question 21.png [ 252.63 KiB | Viewed 7952 times ]

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

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bmwhype2 wrote:
If f(x) = x^2/(x^4 - 1), 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 let's plug in

x = 2

f(2) = 4/15

f(1/2) = 1/4 * 16/-15 = -4/15

f(x) = -f(x)

B
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)?   [#permalink] 04 Feb 2019, 22:27
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