Answer
$f^{-1}(f(A))$ gives the area which can be covered by $f(A)$ gallons; that is, $A$ square feet. Similarly, $f\left(f^{-1}(n)\right)$ gives the number of gallons needed for an area of $f^{-1}(n)$; that is, $n$ gallons.
Work Step by Step
Since $f(A)=A / 250$ and $f^{-1}(n)=250 n$, we have
$$
\begin{aligned}
f^{-1}(f(A)) & =f^{-1}\left(\frac{A}{250}\right)=250 \frac{A}{250}=A . \\
f\left(f^{-1}(n)\right) & =f(250 n)=\frac{250 n}{250}=n .
\end{aligned}
$$
We know that $f(A)$ gives the number of gallons of paint needed to cover an area $A$, and $f^{-1}(n)$ gives the area covered by $n$ gallons. Thus $f^{-1}(f(A))$ gives the area which can be covered by $f(A)$ gallons; that is, $A$ square feet. Similarly, $f\left(f^{-1}(n)\right)$ gives the number of gallons needed for an area of $f^{-1}(n)$; that is, $n$ gallons.
