1. **State the problem:** Find the inverse function of $ f(x) = \frac{7x - 4}{2} $. 2. **Recall the formula and rule:** To find the inverse function $ f^{-1}(x) $, we swap $ x $ and $ y $ in the equation $ y = f(x) $ and then solve for $ y $. 3. **Write the original function:** $ y = \frac{7x - 4}{2} $. 4. **Swap $ x $ and $ y $:** $ x = \frac{7y - 4}{2} $. 5. **Solve for $ y $:** Multiply both sides by 2: $$ 2x = 7y - 4 $$ 6. **Add 4 to both sides:** $$ 2x + 4 = 7y $$ 7. **Divide both sides by 7:** $$ y = \frac{2x + 4}{7} $$ 8. **Show cancellation step:** $$ y = \frac{\cancel{2}x + \cancel{4}}{\cancel{7}} \text{ (no common factors to cancel here, so this is just the fraction)} $$ 9. **Final inverse function:** $$ f^{-1}(x) = \frac{2}{7}x + \frac{4}{7} $$ This means the inverse function is a linear function with slope $ \frac{2}{7} $ and y-intercept $ \frac{4}{7} $.