Which of the following describes all values of x for which

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

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.

The correct answer: E

Hope this helps!

-Jay
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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

Simplifying, we have:

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