A car rental agency charges $\$ 175$ per week plus $\$ 0.20$ per mile to rent a car. a. Express the weekly cost to rent the car, $f$, as a function of the number of miles driven during the week, $x$. b. How many miles did you drive during the week if the weekly cost to rent the car was $\$ 225$ ?

Step 1 ：Express the weekly cost to rent the car, $f$, as a function of the number of miles driven during the week, $x$. The cost is composed of a fixed part, $175$, and a variable part, $0.20$ per mile. So, the cost function can be expressed as \(f(x) = 175 + 0.20x\).

Step 2 ：Find the number of miles driven given the total cost. We can do this by setting the cost function equal to the given cost and solving for $x$.

Step 3 ：Substitute $x = 250$ into the cost function, we get \(f(250) = 175 + 0.20*250 = 225\), which is the given cost.

Step 4 ：The number of miles driven during the week is \(\boxed{250}\).