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GMAT Exam pack 2 - Functions

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by GMATGuruNY » Fri Jun 24, 2016 4:12 am
The function f is defined for all nonzero x by the equation f(x) = x - 1/x. If x ≠ 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)
Let x=2.
Then:
f(1/x) = f(1/2).

The question becomes:
Which of the following equals f(1/2)?

Since f(x) = x - 1/x, we get:
f(1/2) = 1/2 - 1/(1/2) = 1/2 - 2 = -3/2. This is our target.
Now plug x=2 into the answers to see which yields our target of -3/2.

A: f(x)
f(2) = 2 - 1/2 = 3/2.

B: f(-x)
f(-2) = -2 - (1/-2) = -3/2.

C: f(-1/x)
f(-1/2) = -1/2 - (1/(-1/2)) = 3/2.

D: 1/f(x)
Since A indicates that f(x) = 3/2, 1/f(x) = 1/(3/2) = 2/3.

E: -1/f(x)
Since D indicates that 1/f(x) = 2/3, -1/f(x) = -2/3.

Our target of -3/2 is yielded only by B.

The correct answer is B.
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by Brent@GMATPrepNow » Fri Jun 24, 2016 6:03 am
The function f is defined for all nonzero x by the equation f(x) = x - 1/x. If x ≠ 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)
Mitch's INPUT-OUTPUT approach is the fastest. However, we could also PLUG 1/x into the function as see what we get.

Given: f(x) = x - 1/x
So, f(1/x) = 1/x - 1/(1/x)
= 1/x - x

Now check the answer choices:
A) f(x) = x - 1/x Doesn't match. Eliminate A

B) f(-x) = -x - 1/(-x)
= -x + 1/x
= 1/x - x
PERFECT!
So, f(1/x) is the same as f(-x)

For more on dealing with functions on the GMAT, see this video: https://www.gmatprepnow.com/module/gmat ... /video/974

Here's a practice question for reinforcement: https://www.gmatprepnow.com/module/gmat ... /video/975

Cheers,
Brent
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by DavidG@VeritasPrep » Fri Jun 24, 2016 6:11 am
Note, also, that this is a textbook example of why it can be dangerous to set x = 1 in a function question. Obviously f(1/x) and the f(x) will yield the same result, as they're both f(1). [Same for f(-x) and f(-1/x), as they'd both be f(-1), which, in turn, turns out to give you the same result as f(1) for this function.]
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by OptimusPrep » Fri Jun 24, 2016 7:57 pm
lucas211 wrote:Hello BTG

Would appreciate a little help on the following question:

The function f is defined for all nonzero x by the equation f(x) = x - 1/x. If x ≠ 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)

Thanks in advance
f(x) = x - 1/x
f(1/x) = 1/x - x

We can either solve the by putting values or solve algebraically.

A) f(x). This is not equal to f(1/x)

B) f(-x) = -x -(-1/x) = -x + 1/x = f(1/x).
CORRECT answer.
We do not need to check for the other options.

Correct Option: B
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