Chapter 2, Problem 3CT

To determine

The domain of function $g(x)=\frac{x+2}{|x+2|}$, and evaluate function at $x=-1$ .

Answer to Problem 3CT

Solution:

Domain of a function is $\left(-\infty ,-2\right)\cup \left(-2,\infty \right)$ .

The value of $g(-1)=1$ .

Explanation of Solution

Given information:

The function is $g(x)=\frac{x+2}{|x+2|}$ .

Domain is set of $x$ values where the function is defined.

Here, function is defined for all values except $|x+2|=0$ .

Here, function is undefined at $x=-2$ .

Therefore, exclude the point $x=-2$ from domain.

Thus, domain of function in interval notation is $\left(-\infty ,-2\right)\cup \left(-2,\infty \right)$ .

To evaluate function at $x=-1$, substitute $x=-1$ in $g(x)=\frac{x+2}{|x+2|}$ .

Therefore,

  $g(-1)=\frac{-1+2}{|-1+2|}$ ,

  $\Rightarrow g(-1)=\frac{1}{\left|1\right|}=1$ .

The value of $g(-1)=1$ .