Question

You have a coupon for your favorite clothing store for $20 off any purchase of more than $75. The store is

also running a 15%-off sale on its entire inventory. Let x be the original price,
f x( )
be the price with the $20
coupon applied, and
g x( )
be the price with the 15% discount applied.
(a) Write an expression for
f x( ) . (3 points)
(b) Write an expression for
g x( ) . (3 points)
(c) Write the expression
(f g x )( )
and explain what it represents? (3 points)
(d) Write the expression
(g f x )( )
and explain what it represents? (3 points)
(e) If the store allows you to apply both the 15% discount and the $20-off coupon, does it matter which
you apply first? How do you know? (3 points

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

Explanation:

It does not matter which one you apply first.