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

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CEO
Joined: 21 Jan 2007
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Location: New York City
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f(x) = x^2 / (x^4 - 1) What is f(1/x) in terms of f(x)? f -f [#permalink]  16 Nov 2007, 07:16
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]
SVP
Joined: 07 Nov 2007
Posts: 1829
Location: New York
Followers: 26

Kudos [?]: 451 [0], given: 5

Re: f(1/x) [#permalink]  16 Nov 2007, 07:21
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/(1-x^4)= - ( x^2/(x^4-1))
= -f(x)

I pick B.

What is OA?
Director
Joined: 30 Nov 2006
Posts: 592
Location: Kuwait
Followers: 11

Kudos [?]: 154 [0], given: 0

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: 14
Followers: 0

Kudos [?]: 0 [0], given: 0

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)
Director
Joined: 09 Aug 2006
Posts: 767
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Kudos [?]: 49 [0], given: 0

Re: f(1/x) [#permalink]  17 Nov 2007, 00:55
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)

CEO
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Re: f(1/x) [#permalink]  17 Nov 2007, 22:49
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^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.
Re: f(1/x)   [#permalink] 17 Nov 2007, 22:49
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