Question

A store has two different coupons that customers can use. One coupon gives the customer $15 off their purchase, and the other coupon gives the customer 30% off of their purchase. Suppose they let a customer use both coupons and choose which coupon gets applied first. For this context, ignore sales tax.
Let f be the function that inputs a cost (in dollars) and outputs the cost after applying the "$15 off" coupon, and let g be the function that inputs a cost (in dollars) and outputs the cost after applying the "35% off" coupon.
a. Suppose acustomerwants to purchase asi 40 item and apply the si 5 of coupon first, and then the 35% or coupon How much will the item cost after applying the coupons?
b. Suppose a customer wants to purchase a S 140 item and apply the SI 5 off coupon first, and then the 35% or coupon Ure ction notation to represent how much the item will cost (dollars) after applying the coupons.
c. Suppose a customer wants to purchase a $140 item and apply the 35% om coupon first and then the sis of coupon How much will the item cost after applying the coupons?
d. Suppose a customer wants to purchase a S 140 item and apply the "35% or coupon first and then the "S 15 off coupon. Usefu ction notation to represent how much the item will cost (dollars) after applying the coupons.

Answer 1

Answer:

16.25;

g(f(x)) ;

76 ;

f(g(x))

Explanation:

For 15 off

f(x) = x - 15

For 35% off

g(x) = (1 - 0.35)x = 0.65x

g(x) = 0.65x

A.)

For the $15 off coupon :

f(x) = x - 15

f(x) 40 - 15 = 25

For the 35% coupon :

g(x) = (1-0.35)x

g(x) = 0.65(25)

g(x) = 16.25

B.)

Applying $15 off first, then 35%

Here, g is a function of f(x)

g(f(x))

Here g(x) takes in the result of f(x) ;

For the $140 off coupon :

f(x) = x - 15

f(140) = 140 - 15 = 125

For the 35% coupon :

g(125) = (1-0.35)x

g(124) = 0.65(125) = $81.25

C.)

x = 140

g(x) = 0.65x

g(140) = 0.65(140)

g(140) = 91

f(x) = x - 15

f(91) = 91 - 15

f(91) = 76

D.)

Here, F is a function of g(x)

f(g(x))

f(x) = (0.65*140) - 15