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by Brent@GMATPrepNow » Tue May 09, 2017 5:44 am
I've added some brackets to avoid ambiguity.
Hmna wrote:if f(x) = 1/(1-|x|) which of the following is NOT its range?

A)2
B)1.5
C)1
D)0.5
Here's a more GMAT-like wording of the question:
If y = 1/(1-|x|), which of the following is NOT a possible value of y?
Answer: D
If 0.5 = 1/(1-|x|), then |x| must equal -1. However, |x| will be greater than or equal to 0 for all values of x.
So, 1/(1-|x|) can never equal 0.5

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Brent
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by Matt@VeritasPrep » Thu May 11, 2017 8:49 pm
We could also just try to solve for each answer.

(A):

1 / (1 - |x|) = 2

1 = 2 * (1 - |x|)

1 = 2 - 2|x|

2|x| = 1

|x| = 1/2

so x = 1/2 or -1/2

(B)

1 / (1 - |x|) = 1.5

1 = 1.5 - 1.5|x|

1.5|x| = .5

|x| = 1/3

(C)

1 / (1 - |x|) = 1

1 = 1 - |x|

|x| = 0

A, B, and C are all possible, so D must be the answer.
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