Question

PLEASE HELP

A car dealer offers a 15% discount off the list price x for any car on the lot. At the same time, the manufacturer offers a $1500 rebate for each purchase of a car.


a. Write a function f(x) to represent the price after the discount is applied.


b. Write a function g(x) to represent the price after the rebate is applied.


Suppose the list price of a car is $19,000. Use a composite function to find the price

of the car:


C. if the discount is applied before the rebate;


D. if the rebate is applied before the discount

Answer 1

A) f(x) = 0.85x

B) g(x) = x - 1500

C) g(f(x)) = $14650

D) f(g(x)) = $14875

Explanation:

A) The list price is x and a 15% discount is applied.

Thus;

f(x) = x - 15%x

f(x) = 0.85x

B) We are told that the manufacturer offers a $1500 rebate for each purchase of a car.

Thus, the function g(x) to represent the price after the rebate is applied is;

g(x) = x - 1500

C)if the discount is applied before the rebate, the function is;

g(f(x))

Now,

f(x) = 0.85(19000)

f(x) = 16150

g(x) = x - 1500

Thus;

g(x) = 16150 - 1500

g(x) = $14650

D) If discount after rebate, then we have; f(g(x))

g(x) = 19000 - 1500

g(x) = 17500

f(g(x)) = 0.85(17500)

f(g(x)) = $14875