A car dealership is offering $1,500 cash back on the purchase of a new vehicle. The cost, after the cash back, of a new vehicle can be modeled by the function C(x) = x – 1,500, where x is the original price of the vehicle. The vehicle is subject to a sales tax of 8.43%, so the total price of the vehicle is represented by the function P(C) = 1.0843C.
Answer
A
C(P(x)) = 1.0843x – 1,500
B
C(P(x)) = 1.0843x – 1,626.45
C
P(C(x)) = 1.0843x – 1,500
D
P(C(x)) = 1.0843x – 1,626.45
Explanation
First apply the cash-back function: C(x) = x − 1,500. Then apply the sales-tax function: P(C(x)) = 1.0843(x − 1,500) = 1.0843x − 1,626.45, so the correct choice is P(C(x)) = 1.0843x − 1,626.45.
AI-written and checked against the verified answer.