# How do you find the domain of f(x) = (x-4)/(x+3)?

Jun 11, 2018

$\left(- \infty , - 3\right) U \left(- 3 , \infty\right)$

#### Explanation:

When dealing with rational functions $f \left(x\right) = \frac{p \left(x\right)}{q \left(x\right)}$ , our domain, that is, values of $x$ for which $f \left(x\right)$ exists, excludes any values that cause $q \left(x\right) = 0.$

This is because division by $0$ isn't possible, so the function won't have any real value at these values of $x$.

For $f \left(x\right) = \frac{x - 4}{x + 3} ,$ we have the form $\frac{p \left(x\right)}{q \left(x\right)} ,$ where $p \left(x\right) = x - 4 , q \left(x\right) = x + 3$

Set $q \left(x\right) = 0$ and solve for $x$:

$x + 3 = 0$
$x = - 3$

So, our domain excludes $x = - 3$.

In interval form, the domain is

$\left(- \infty , - 3\right) U \left(- 3 , \infty\right)$