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If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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Updated on: 25 Sep 2014, 23:43
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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)
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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.




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Re: If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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17 Nov 2007, 01:55
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)
answer B.




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Re: If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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16 Nov 2007, 08:21
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/(1x^4)=  ( x^2/(x^41))
= 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)?
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16 Nov 2007, 12:57
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 ?



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Re: If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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16 Nov 2007, 13:14
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 * (1x^4)
= f(x) * (x2/ x2)
= 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)?
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17 Nov 2007, 23:49
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^41) > (1/x^2)/(1x^4)/(x^4) > just cancel out the x's. we get x^2/(1x^4) > x^2/(x^41) > (x^2)/(x^41)
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.
4/161 > 4/15
Then (1/4)/(1/161) > 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)?
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25 Sep 2014, 22:58
\(f(x) = \frac{x^2}{x^4  1}\) \(\frac{1}{f(x)} = \frac{x^4  1}{x^2} = x^2  \frac{1}{x^2}\) \(\frac{1}{f(\frac{1}{x})} = \frac{1}{x^2}  x^2 = \frac{1}{f(x)}\) \(f(\frac{1}{x}) = f(x)\) Answer = B
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Re: If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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25 Sep 2014, 23:37
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) Check other Functions questions in our Special Questions Directory.
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Re: If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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02 Jan 2015, 06:03
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) answer B. 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)?
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02 Jan 2015, 11:03
Can someone explain the answer to this question with the number picking technique?
For example x=2?



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Re: If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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02 Jan 2015, 13:38
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). Final Answer: GMAT assassins aren't born, they're made, Rich
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If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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06 Mar 2015, 08:49
\(f(x) = x^2/(x^41)\) that means that\(f(1/x) = (x^41)/x^2\)
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)?
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06 May 2015, 14:03
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)?
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03 Oct 2015, 10:47
f(1/x)= (1/x ^ 2)/((1/x) ^4 1) = (1/x ^ 2)/((1x^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)?
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18 Jul 2017, 22:04
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. https://www.youtube.com/watch?v=T6Zdr5w_bE
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Re: If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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04 Feb 2019, 22:27
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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Re: If f(x) = x^2/(x^4  1), what is f(1/x) in terms of f(x)?
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