functions inverse

Question

look back to question 2 of the practice problems. suppose the 20% discount is applied first when using both coupons. write a composition function that gives the final cost of an item if both coupons are used. with this function, find the final cost of a pair of shoes that originally cost $100.

lanie has two coupons for a shoe store, one is $15 off and the other is 20% off coupon. a) let p represent the original price of an item. write a function, f(p) , that gives a final cost of a item of price p if she uses only the $15 off coupon. b) write a function, g(p) , that gives the final cost of she only uses the 20% off coupon. c) when using both coupons, the $15 off discount is applied first, then the 20% off is applied second. write a composite function that gives the final cost of an item if both coupons are used.

Answer 1

f(p) = p - 15

g(p) = 0.8 * p

using the 20% coupon first,

C(p) = f(g(p)) = 0.8*p - 15

C(100) = 0.8*100 - 15 = 80 - 15 = 65