1. **State the problem:** Find the inverse of the function $f(x) = 2x - 3$. 2. **Formula and rule:** To find the inverse function $f^{-1}(x)$, swap $x$ and $y$ in the equation and solve for $y$. 3. **Step-by-step:** - Start with $y = 2x - 3$. - Swap $x$ and $y$: $x = 2y - 3$. - Solve for $y$: $$x + 3 = 2y$$ $$y = \frac{x + 3}{2}$$ 4. **Conclusion:** The inverse function is $$f^{-1}(x) = \frac{x + 3}{2}$$. This means to reverse the effect of $f(x)$, add 3 to the input and then divide by 2.