1. Problem: Find the inverse of the function $f(x) = 3x + 7$. 2. To find the inverse, replace $f(x)$ with $y$: $$y = 3x + 7$$ 3. Swap $x$ and $y$ to find the inverse function: $$x = 3y + 7$$ 4. Solve for $y$: $$x - 7 = 3y$$ $$y = \frac{x - 7}{3}$$ 5. Therefore, the inverse function is: $$f^{-1}(x) = \frac{x - 7}{3}$$ This process involves swapping the roles of $x$ and $y$ and then isolating $y$ to express the inverse function.