1. **Problem statement:** Fatema's distance from Tomsville after $t$ hours is given by the function $$D(t) = 15.5 - 5t.$$ We are asked to find the inverse function $D^{-1}(x)$ and interpret it. 2. **Understanding the inverse function:** Given $x = D(t)$, the inverse function $D^{-1}(x)$ gives the value of $t$ such that $D(t) = x$. In other words, $D^{-1}(x)$ tells us the amount of time Fatema has walked when she is $x$ kilometers from Tomsville. 3. **Answer to part (a):** The best description of $D^{-1}(x)$ is: "The amount of time she has walked (in hours) when she is $x$ kilometers from Tomsville." 4. **Finding the inverse function $D^{-1}(x)$:** Start with the equation: $$x = 15.5 - 5t$$ Solve for $t$: $$5t = 15.5 - x$$ $$t = \frac{15.5 - x}{5}$$ Thus, $$D^{-1}(x) = \frac{15.5 - x}{5}$$ 5. **Evaluating $D^{-1}(8.5)$:** Substitute $x = 8.5$: $$D^{-1}(8.5) = \frac{15.5 - 8.5}{5} = \frac{7}{5} = 1.4$$ This means Fatema has walked 1.4 hours when she is 8.5 kilometers from Tomsville. **Final answers:** (a) The amount of time she has walked (in hours) when she is $x$ kilometers from Tomsville. (b) $$D^{-1}(x) = \frac{15.5 - x}{5}$$ (c) $$D^{-1}(8.5) = 1.4$$