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)

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?

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)

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

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

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

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

Answer = B
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how , f(1/x) = -4/15

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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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

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