Chapter 1.4, Problem 1QR

Solution

To find: The domain of a function in interval notation.

The domain D of the function $f\left(x\right)=\frac{x-2}{x+3}$ in interval notation is $D\text{=}\left(-\infty ,-3\right)\cup \left\{-3,\infty \right\}$ .

Given information: The function is $f\left(x\right)=\frac{x-2}{x+3}$

Method/Formula used:

Suppose $y=f\left(x\right)$ be a function $f:A\to B$ , $x\in A,y\in B$ the set A is called the domain of function f and set B the co-domain. Thus, the domain of a function $f\left(x\right)$ are the values of x for which the function $f\left(x\right)$ is defined.

  

Calculation:

The given function is $f\left(x\right)=\frac{x-2}{x+3}$ . This function is not defined when $x+3=0$ or $x=-3$ . For other values of x from the set of real numbers $ℝ\text{or}\left(-\infty ,\infty \right)$ , $f\left(x\right)=\frac{x-2}{x+3}$ is defined. Therefore, the domain D of the function $f\left(x\right)=\frac{x-2}{x+3}$ is the set that in interval notation can be written as $D\text{=}\left(-\infty ,\infty \right)-\left\{-3\right\}$ or $D\text{=}\left(-\infty ,-3\right)\cup \left\{-3,\infty \right\}$ .