You have a coupon for your favorite clothing store for $25 off any purchase of more than $50. The store is also running a 20%-off sale on its entire inventory. Let x be the original price, f (x) be the price with the $25 coupon applied, and g (x) be the price with the 20% discount applied.

a. Write an expression for f (x).

b. Write an expression for g (x).

c. What would the expression (f o g) (x) represent?

d. What would the expression (g o f) (x) represent?

e. If the store allows you to apply both the 20% discount and the $25-off coupon, does it matter which you apply first? How do y

Question

Mathematics

Alyssa Ware

28 March, 08:14

You have a coupon for your favorite clothing store for $25 off any purchase of more than $50. The store is also running a 20%-off sale on its entire inventory. Let x be the original price, f (x) be the price with the $25 coupon applied, and g (x) be the price with the 20% discount applied.

a. Write an expression for f (x).

b. Write an expression for g (x).

c. What would the expression (f o g) (x) represent?

d. What would the expression (g o f) (x) represent?

e. If the store allows you to apply both the 20% discount and the $25-off coupon, does it matter which you apply first? How do y

+3

Answers (1)

Know the Answer?

Lance Barton · Answer 1

F (x) = (1 - 0.25) x = 0.75x

f (x) = 0.75x

g (x) = (1 - 0.2) x = 0.8x

g (x) = 0.8x

(f o g) (x) = f (g (x)) = 0.75 (0.8x) = 0.6x

(f o g) (x) = 0.6x

(g o f) (x) = 0.8 (0.75x) = 0.6x

(g o f) (x) = 0.6x

It does not matter which one you apply first.