1. **State the problem:** Find the inverse of the function $f(x) = 3x - 6$. 2. **Recall the formula for inverse functions:** To find the inverse $f^{-1}(x)$, swap $x$ and $y$ in the equation and solve for $y$. 3. **Write the function with $y$:** $$y = 3x - 6$$ 4. **Swap $x$ and $y$:** $$x = 3y - 6$$ 5. **Solve for $y$:** Add 6 to both sides: $$x + 6 = 3y$$ Divide both sides by 3: $$\frac{x + 6}{3} = y$$ Show cancellation: $$y = \frac{\cancel{3} \cdot \frac{x + 6}{\cancel{3}}}{1} = \frac{x + 6}{3}$$ 6. **Write the inverse function:** $$f^{-1}(x) = \frac{x + 6}{3}$$ 7. **Interpretation:** The inverse function reverses the effect of $f(x)$, so applying $f^{-1}$ to $f(x)$ returns the original input $x$. **Final answer:** $$f^{-1}(x) = \frac{x + 6}{3}$$