Answer
$f^{-1}(x)=\dfrac{-x-6}{2}$
Work Step by Step
The given function, $
f(x)=-2x-6
,$ is equivalent to
\begin{array}{l}\require{cancel}
y=-2x-6
.\end{array}
Interchanging the $x$ and $y$ variables and then solving for $y$ result to
\begin{array}{l}\require{cancel}
x=-2y-6
\\\\
2y=-x-6
\\\\
y=\dfrac{-x-6}{2}
.\end{array}
Hence, the inverse is $
f^{-1}(x)=\dfrac{-x-6}{2}
.$
In the graph above, the black graph is the graph of $f(x)$ and the red graph is the graph of $f^{-1}(x).$
