Question

find the domain of the function. (u(x)=sqrt{-x}-3). write your answer as an inequality. or, you may instead click on \empty set\ or \all reals\ as the answer.

Explanation:

Step1: Recall domain - rule for square - root

For $\sqrt{a}$ to be a real number, $a\geq0$. In the function $u(x)=\sqrt{-x}-3$, we need $-x\geq0$.

Step2: Solve the inequality

Multiply both sides of $-x\geq0$ by $- 1$. When we multiply an inequality by a negative number, the direction of the inequality sign changes. So we get $x\leq0$.

Answer:

$x\leq0$