Answer
$f^{-1}(x)=-\displaystyle \frac{1}{2}x-3$
Work Step by Step
Step 1: Replace $f(x)$ with $y$.
$y=-2x-6$
Step 2: Interchange $x$ and $y$.
$x=-2y-6$
Step 3: Solve the equation for $y$.
$ x=-2y-6,\qquad$ ... add $6$,
$ x+6=-2y,\qquad$ ... multiply with $(-\displaystyle \frac{1}{2})$
$-\displaystyle \frac{1}{2}x-3=y$
Step 4: Replace y with the notation $f^{-1}(x)$.
$f^{-1}(x)=-\displaystyle \frac{1}{2}x-3$
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