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The function f is defined for all nonzero x by the equation

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by NandishSS » Wed Aug 24, 2016 7:46 am
The function f is defined for all nonzero x by the equation f (x) = x - (1/x) . If x not equal to 0, which of the following equals f (1/ X ) ?

A)f(x)
B)f(-x)
C)f(-1/x)
D)1/f(x)
E)-1/f(x)

Source:GMATPrep EP 2

OA:B
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by [email protected] » Wed Aug 24, 2016 9:06 am
Hi NandishSS,

This question can be solved by TESTing VALUES.

We're told that f(X) = X - (1/X) and that X does not equal 0. We're asked for the value of f(1/X).

IF....
X = 2
f(1/2) = 1/2 - (1/(.5) = 1/2 - 2 = -3/2

So we're looking for an answer that equals -3/2 when we plug X=2 into the answers...

Answer A: f(2) = 2 - 1/2 = 3/2 NOT a match
Answer B: f(-2) = -2 - (1/-2) = -3/2 This IS a match
Answer C: f(-1/2) = -.5 - (1/-.5) = -5/2 NOT a match

We can use the calculation from Answer A to deal with Answers D and E....
Answer D: 1/f(2) = 1/(3/2) = 2/3 NOT a match
Answer E: -1/f(2) = -1/(3/2) = -2/3 NOT a match

Final Answer: B

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Rich
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by Scott@TargetTestPrep » Fri Aug 26, 2016 1:35 pm
NandishSS wrote:The function f is defined for all nonzero x by the equation f (x) = x - (1/x) . If x not equal to 0, which of the following equals f (1/ X ) ?

A)f(x)
B)f(-x)
C)f(-1/x)
D)1/f(x)
E)-1/f(x)
Since f(x) = x - (1/x), replacing x with 1/x, we have f(1/x) = (1/x) - (1/(1/x)).

That is, f(1/x) = (1/x) - x.

Let's now review the answer choices to see which one is equivalent to (1/x) - x. .

A) f(x)

f(x) = x - (1/x)

Since f(x) = x - (1/x), answer choice A is not equivalent to (1/x) - x.

B) f(-x)

f(-x) = (-x) - (1/(-x))

-x + 1/x

1/x - x.

Since f(-x) = 1/x - x, answer choice B is equivalent to (1/x) - x.

Answer: B

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by Matt@VeritasPrep » Thu Sep 01, 2016 5:49 pm
f(1/x) =

(1/x) - (1/(1/x)) =

(1/x) - x

This is the original function, but backwards! So we multiplied by a negative, which is equivalent to f(-x), or

f(-x) =

-x - (1/-x) =

-1 + (1/x)

These are the same thing, so f(1/x) = f(-x), and we're set!
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