Question

Find the domain of the function.
Write your answer as an inequality.
Or, you may instead write "Empty set" or "All reals" as the answer.

Answer 1

When taking square roots, you can't take square roots of negative roots of negative numbers. So, what will work for the domain of u(x) is what makes u(x) zero or more. We can make an inequality for that.

u(x) ≥ 0.

$\sqrt{9x+27} \geq 0$

9x + 27 ≥ 0 by squaring both sides

9x ≥ -27

x ≥ -3

So the domain of the function is when x ≥ -3 is true.