Answer
$(-\infty,6) \cup (6,\infty)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(x)=\dfrac{9}{x+6}
,$ is all values of $x$ for which the denominator is not $0.$ Express the answer in interval notation.
$\bf{\text{Solution Details:}}$
Since the denominator of the given function cannot be $0$, then
\begin{array}{l}\require{cancel}
x+6\ne0
\\\\
x\ne-6
.\end{array}
Hence the domain is $
(-\infty,6) \cup (6,\infty)
.$