Question

Hiro has a $5 off coupon for his favorite electronics store. The store is currently running a 10% off sale on all items. If the function representing the $5 off coupon is c(x) = x − 5, and the function s (x) = 0.9x​ represents the 10% off sale, what composite function represents the purchase price if the 10% off is applied before the coupon?

Answer 1

You can compose functions c(x) and s(x) in two ways:
1. c(s(x))=0.9x-5 
and 
2. s(c(x))=0.9(x-5).
The main difference between these two function is the sequence of actions performed. In first case 10% off is applied before the coupon and in second case 10% off is applied after the coupon.
Answer: c(s(x))=0.9x-5