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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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bmwhype2
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If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)? [#permalink] New post   Updated on: 18 Oct 2023, 00:39
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If \(f(x) = \frac{x^2}{x^4 - 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)


B. \(-f(x)\)


C. \(\frac{1}{f(x)}\)


D. \(-\frac{1}{f(x)}\)


E. \(2f(x)\)

M15-17

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B

Originally posted by bmwhype2 on 16 Nov 2007, 08:16.
Last edited by Bunuel on 18 Oct 2023, 00:39, edited 4 times in total.
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PareshGmat
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Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)? [#permalink] New post   25 Sep 2014, 22:58
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\(f(x) = \frac{x^2}{x^4 - 1}\)

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

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

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

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)? [#permalink] New post   02 Jan 2015, 13:38
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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).

Final Answer:
Show Spoiler
B


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x2suresh
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Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)? [#permalink] New post   16 Nov 2007, 08:21
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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]


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] New post   17 Nov 2007, 01:55
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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)

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)? [#permalink] New post   25 Sep 2014, 23:37
Expert Reply
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)? [#permalink] New post   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)? [#permalink] New post   18 Jul 2017, 22:04
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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.

https://www.youtube.com/watch?v=T6-Zdr5w_bE
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Bunuel
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Re: If f(x) = x^2/(x^4 - 1), what is f(1/x) in terms of f(x)? [#permalink] New post   07 Oct 2023, 10:31
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If \(f(x) = \frac{x^2}{x^4 - 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)


B. \(-f(x)\)


C. \(\frac{1}{f(x)}\)


D. \(-\frac{1}{f(x)}\)


E. \(2f(x)\)


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

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

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

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

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

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

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

\(=-f(x)\).


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)? [#permalink]
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