Question

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

role="math" localid="1645959311185" $g\left(x\right)=\frac{x+2}{\left|x+2\right|}$

Short answer

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

The value at$x=-1$is$1$.

Step-by-step solution

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 

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