Chapter 1.8, Problem 64E

Consumer Awareness The suggested retail price of a new hybrid car is p dollars. The dealership advertises a factory rebate of $\$2000$ and a $10\%$ discount.

(a) Write a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory.

(b) Write a function S in terms of p giving the cost of the hybrid car after receiving the dealership discount.

(c) Find and interpret $\left(R\circ S\right)\left(p\right)\text{ and }\left(S\circ R\right)\left(p\right).$

(d) Find $\left(R\circ S\right)\left(25,795\right)\text{ and }\left(S\circ R\right)\left(25,795\right).$ Which yields the lower cost for the hybrid car? Explain.