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bmwhype2
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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\(f(x) = \frac{x^2}{x^4 - 1}\)

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

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

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

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

For example x=2?
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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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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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