Question

Find the domain of the rational function. f(x)=x−2/x+3Enter your answer in interval notation.

Answer 1

Given

The rational function,

$f(x)=\frac{x-2}{x+3}$

To find:

The domain of the rational function.

Explanation:

It is given that,

$f(x)=\frac{x-2}{x+3}$

That implies,

Set the denominator equal to 0.

Then,

$\begin{gathered} x+3=0 \\ x=-3 \end{gathered}$

Therfore, the domain of the function is,

$\begin{gathered} Domain:\lbrace x\in R:x\ne-3\rbrace \\ \Rightarrow(-\infty,\infty)=R \\ \because x\ne-3 \\ \Rightarrow x\in(-\infty,-3)\text{ }or\text{ }(-3,\infty) \\ \Rightarrow x\in(-\infty,-3)\cup(-3,\infty) \end{gathered}$

Hence, the interval notation of the domain is

$(-\infty,-3)\cup(-3,\infty)$