Question

Dishwashers are on sale for 25% off the original price (d), which can be expressed with the function p(d) = 0.75d. Local taxes are an additional 14% of the discounted price, which can be expressed with the function c(p) = 1.14p. Using this information, which of the following represents the final price of a dishwasher with the discount and taxes applied?
c(p) ⋅ p(d) = 0.855pd
c(p) + p(d) = 1.89d
c[p(d)] = 0.855d
d[c(p)] = 1.89p

Answer 1

We are given the functions:

P (d) = 0.75 d                                      ---> 1

C (P) = 1.14 P                                      ---> 2

The problem asks us to find for the final price after discount and taxes applied; therefore we have to find the composite function of the two given functions 1 and 2. To solve for composite function of the final price of the dishwasher with the discount and taxes applied, all we have to do is to plug in the value of P (d) with variable d into the equation of C (P). That is:

C (P) = 1.14 (0.75 d)

C (P) = 0.855 d

or

C [P (d)] = 0.855 d