Q. 60 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 47– 62, find the domain of each function. 

$q\left(x\right) =\sqrt{-x-2}$

Step-by-Step Solution

Answer

The domain of the given function is $\left\{x\right|x\le -2\}$

Step 1. Given Information

In the given problems we have to find the domain of given function.

$q\left(x\right) =\sqrt{-x-2}$

Step 2. The function q tells us to take the square root of - x - 2 .

But only non-negative numbers have real square roots, so the expression under the square root (the radicand) must be non-negative (greater than or equal to zero).

Step 3. This requires that

$-x-2\ge 0$

Add 2 on both side

$$\begin{gathered} -x-2+2\ge 0+2 \\ -x\ge 2 \end{gathered}$$

Multiply with $-1$ on both side and change the inequality

$$\begin{gathered} -x\times (-1)\le 2\times (-1) \\ x\le -2 \end{gathered}$$

Step 4. The domain of q is

$\left\{x\right|x\le -2\}$