Which of the following describes all values of x for which 1-x^2 >= 0?
(A) x >= 1
(B) x <= -1
(C) 0 <= x <= 1
(D) x <= -1 or x >= 1
(E) -1 <= x <= 1
OA E
Source: Official Guide
Which of the following describes all values of x for which
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A
B
C
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E
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- Jay@ManhattanReview
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We are given that 1 - x^2 ≥ 0 => 1 ≥ x^2. This implies that the absolute value of x must not exceed 1. Thus, we have -1 ≤ x ≤ 1.BTGmoderatorDC wrote:Which of the following describes all values of x for which 1-x^2 >= 0?
(A) x >= 1
(B) x <= -1
(C) 0 <= x <= 1
(D) x <= -1 or x >= 1
(E) -1 <= x <= 1
OA E
Source: Official Guide
The correct answer: E
Hope this helps!
-Jay
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Simplifying, we have:BTGmoderatorDC wrote:Which of the following describes all values of x for which 1-x^2 >= 0?
(A) x >= 1
(B) x <= -1
(C) 0 <= x <= 1
(D) x <= -1 or x >= 1
(E) -1 <= x <= 1
OA E
Source: Official Guide
1 ≥ x^2
√1 ≥ √x^2
1 ≥ |x|
Now we solve for x:
When x is positive:
1 ≥ |x|
1 ≥ x
x ≤ 1
This can be re-expressed as x ≤ 1.
When x is negative:
1 ≥ |x|
1 ≥ -x
-1 ≤ x
We combine the two resulting inequalities to get:
-1 ≤ x ≤ 1
Answer: E
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