Answer
$f(100)$ tells us how much paint is needed for $100 \mathrm{ft}^2$.
$f^{-1}(100)$ represents the area which can be painted by 100 gallons
Work Step by Step
Since $n=f(A)$, in $f(100)$ we have $A=100 \mathrm{ft}^2$. Evaluating $f(100)$ tells us how much paint is needed for $100 \mathrm{ft}^2$. Since
$$
n=f(100)=\frac{100}{250}=0.4
$$
it takes 0.4 gallon of paint to cover $100 \mathrm{ft}^2$.
In $f^{-1}(100)$, the 100 is the number of gallons, so $f^{-1}(100)$ represents the area which can be painted by 100 gallons:
$$
A=f^{-1}(100)=250 \cdot 100=25,000 \mathrm{ft}^2 .
$$
