Answer: C) All real values of x such that [tex]x \le 0[/tex]
In other words, x must be 0 or smaller.
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Explanation:
The reason why is because we must make the stuff under the square root to never be negative. We must make -2x be 0 or larger.
So,
[tex]-2x \ge 0 \\\\-2x+2x \ge 0+2x \ \text{ ... add 2x to both sides}\\\\0 \ge 2x\\\\2x \le 0 \ \text{ ... flip both sides, and the inequality sign}\\\\x \le 0/2 \ \text{ ... divide both sides by 2}\\\\x \le 0[/tex]
As an example, if x = -2, then -2x = -2(-2) = 4 is positive. Applying the square root to a positive number is valid.
But if x = 5, then -2x = -2*5 = -10 is under the square root, which is not allowed.