1. **State the problem:** Find the inverse function of $f(x) = 3x + 1$. 2. **Formula and rules:** To find the inverse function $f^{-1}(x)$, we swap $x$ and $y$ in the equation and solve for $y$. 3. **Step-by-step solution:** Start with $y = 3x + 1$. Swap $x$ and $y$: $$x = 3y + 1$$ Solve for $y$: $$x - 1 = 3y$$ Write the division step showing cancellation: $$\frac{x - 1}{\cancel{3}} = \cancel{3}y \implies y = \frac{x - 1}{3}$$ 4. **Final answer:** The inverse function is $$f^{-1}(x) = \frac{x - 1}{3}$$. This means to reverse the effect of $f(x)$, subtract 1 from the input and then divide by 3.