#### Answer

$f^{-1} (x) = x+6$

#### Work Step by Step

$f (x) = x-6$
Step 1: Replace $f (x)$ with $y$.
$$y = x-6$$
Step 2: Interchange $x$ with $y$.
$$x = y-6$$
Step 3: Solve for $y$.
$$y = x+6$$
Step 4: Replace $y$ with $f^{-1} (x)$.
$$f^{-1} (x) = x+6$$