Chapter 4.1, Problem 89PE

(a)

To determine

To calculate: A function representing the total amount of property tax $T\left(x\right)$ for a home with a taxable value of $x$ thousand dollars, if the millage rate is the amount of property tax per $\$1000$ of the taxable value of a home. For a certain country, the millage rate is $24$ mil. A city within the country also imposes a flat fee of $\$108$ per home.

(b)

To determine

To calculate: An equation for $T^{-1}\left(x\right)$ of the function, $T\left(x\right)=24x+108$.

(c)

To determine

What does the inverse function $T^{-1}\left(x\right)=\frac{x-108}{24}$ represent in the context of the problem.

(d)

To determine

To calculate: The value of $T^{-1}(2988)$ for the function, $T^{-1}\left(x\right)=\frac{x-108}{24}$.