if f(x)=1/1-|x|which of the following is NOT its range?
A)2
B)1.5
C)1
D)0.5
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Brent@GMATPrepNow
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I've added some brackets to avoid ambiguity.
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
Cheers,
Brent
Here's a more GMAT-like wording of the question: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
Answer: DIf y = 1/(1-|x|), which of the following is NOT a possible value of y?
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
Cheers,
Brent
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Matt@VeritasPrep
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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.
(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.
