Question

The millage rate is the amount of property tax per $1000 of the taxable value of

a home. For a certain county the millage rate is 29 mil. A city within the county
also imposes a flat fee of $101 per home.
a. Write a function representing the total amount of property tax T(x) for a home
with a taxable value of x thousand dollars.
b. Write an equation for T
-1(x).
c. What does the inverse function represent in the context of this problem?

Answer 1

9514 1404 393

Answer:

a. T(x) = 29x +101

b. T^-1(x) = (x -101)/29

c. the value of the home in thousands as a function of the tax on it

Explanation:

a. The tax is $101 plus $29 per thousand of value. x is the value in thousands, so the tax is ...

T(x) = 29x +101

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b. The inverse function can be found by solving ...

x = T(y)

x = 29y +101

x -101 = 29y

y = (x -101)/29

T^-1(x) = (x -101)/29

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c. The function tells you the tax on a home worth x thousands.

The inverse function tells you the worth of the home in thousands when the tax on it is x.