Use composition of functions to find the sale price of a $90 purchase when the $5 off discount is applied prior to the 15% off discount.

Answer 1

Both adds are used.

First deduct 15% from the original.

Next take off $5.

So: 90*.85-5=71.5

Answer 2

Without actually writing the functions, it might be clearer. We have 90 dollars and first apply the 5 dollar discount, leading to 85 dollars. Then, we apply the 15% discount to the already discounted 85 giving us .85 * 85 = $72.25

However, because it says to use a composition of functions, I think we should start by writing the two discount functions.

Let D(x) be the function modeling the 5 dollar discount (D for dollar) and P(x) be the function modeling the 15 percent discount (P for discount).

D(x) = x-5, a simple 5 dollar saving and P(x) = (1-.15) x = .85 x, a 15 percent price reduction.

If the 5 dollars off is recorded before the 15% off, our total discounted price function should be P(D(x)) = .85(x-5).

Since x = starting price = 90$ we have P(D(x)) = .85 * 85 = $72.25