Question

What is the domain of the function f(x) = x+ 2? ​

Answer 1

Correctttttttttttrtttttttttttttt

Answer 2

Answer:  Choice D) $x \ge -6$

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Explanation:

Taking the square root of a negative number leads to a nonreal result.

So we want the radicand to be 0 or positive

Set the stuff under the square root to be 0 or larger. Solve for x.

$\frac{1}{3}x+2 \ge 0\\\\\frac{1}{3}x \ge 0-2\\\\\frac{1}{3}x \ge -2\\\\x \ge 3(-2)\\\\x \ge -6$

If x is -6 or larger, then $\frac{1}{3}x+2$ is 0 or larger leading to some real number for f(x).

The inequality sign does not flip because we multiplied both sides by a positive number. The inequality sign only flips when we multiply both sides by a negative number.