Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of each function and evaluate each function at $x=-1$.

$g\left(x\right)=\frac{x+2}{\left|x+2\right|}$

Step-by-Step Solution

Answer

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

The value at $x=-1$ is $1$.

Step 1. Find the domain of the function.

$g\left(x\right)=\frac{x+2}{\left|x+2\right|}$

For domain, denominator cannot be zero.

So,

$$\begin{gathered} \left|x+2\right|\ne 0 \\ x+2\ne 0 \\ x\ne -2 \end{gathered}$$

Therefore, the domain of the function is $x$ belongs to all real numbers except $-2$.

Step 2. Find value of g ( x ) at x = - 1

$$\begin{gathered} g\left(x\right)=\frac{x+2}{\left|x+2\right|} \\ g(-1)=\frac{-1+2}{\left|-1+2\right|} \\ g(-1)=\frac{1}{\left|1\right|} \\ g(-1)=1 \end{gathered}$$