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