1. **State the problem:** Find the inverse function of $f(x) = \frac{3}{4}x + 2$. 2. **Recall the formula:** To find the inverse, swap $x$ and $y$ and solve for $y$. If $y = f(x)$, then $x = f^{-1}(y)$. 3. **Write the function with $y$:** $$y = \frac{3}{4}x + 2$$ 4. **Swap $x$ and $y$:** $$x = \frac{3}{4}y + 2$$ 5. **Solve for $y$:** Subtract 2 from both sides: $$x - 2 = \frac{3}{4}y$$ 6. **Isolate $y$ by dividing both sides by $\frac{3}{4}$:** $$y = \frac{x - 2}{\frac{3}{4}}$$ 7. **Simplify the division by a fraction:** $$y = (x - 2) \times \frac{4}{3}$$ 8. **Final inverse function:** $$f^{-1}(x) = \frac{4}{3}(x - 2)$$ This means the inverse function reverses the effect of $f(x)$ by first subtracting 2 and then multiplying by $\frac{4}{3}$.