To find the inverse of the function $g(x) = -3(x + 6)$, we need to follow these steps:

1. Rewrite the function in terms of $y$: $y = -3(x + 6)$

2. Switch $x$ and $y$ to find the inverse: $x = -3(y + 6)$

3. Solve for $y$:

   • First, divide both sides by $-3$: $\frac{x}{-3} = y + 6$
   • Simplify the division: $-\frac{x}{3} = y + 6$
   • Subtract 6 from both sides to solve for $y$: [ y = -\frac{x}{3} - 6