1. **State the problem:** Find the inverse of the function $f(x) = \frac{1}{3}x - 1$. 2. **Recall the formula and rule:** To find the inverse function $f^{-1}(x)$, we swap $x$ and $y$ in the equation and then solve for $y$. 3. **Write the original function with $y$:** $$y = \frac{1}{3}x - 1$$ 4. **Swap $x$ and $y$:** $$x = \frac{1}{3}y - 1$$ 5. **Solve for $y$:** Add 1 to both sides: $$x + 1 = \frac{1}{3}y$$ Multiply both sides by 3: $$3(x + 1) = y$$ 6. **Simplify:** $$y = 3x + 3$$ 7. **Conclusion:** The inverse function is $$f^{-1}(x) = 3x + 3$$ This means the inverse of $f(x) = \frac{1}{3}x - 1$ is $f^{-1}(x) = 3x + 3$. Note: The original guess $g(x) = | y = 3x + 3$ is incorrect because of the absolute value symbol; the correct inverse does not have absolute value.