4. The Best Elect electronics store is having a sale on November 8th on any new electronics purchased. Every customer will receive $50 off their purchase of a new electronic item. They are also offering a student discount on every item in the store for the whole month of November. If you can prove you are a student, you will receive 15% off any item. Let x be the price of any new electronic item in the store. a. Write a function P(x) that represents the price of a new electronic item on November 8th for any customer. b. Write a function D(x) that represents the price you will pay for an item after the student discount is applied during any day in November.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.7P
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4. The BestElect electronics store is having a sale on November 8th on any new electronics purchased. Every
customer will receive $50 off their purchase of a new electronic item. They are also offering a student discount
on every item in the store for the whole month of November. If you can prove you are a student, you will
receive 15% off any item. Let x be the price of any new electronic item in the store.
a. Write a function P(x) that represents the price of a new electronic item on November 8th for any
customer.
b. Write a function D(x) that represents the price you will pay for an item after the student discount is
applied during any day in November.
Now, we have two functions P and D that depend on the price of the item, x. P is a rule that says "take the price of the
item, then subtract $50." D is a rule that says "take the price, then take 85% of it." If you want to take advantage of both
sales, a composition of functions is necessary! But is there a difference between P(D(x)) and D(P(x))?
a. What does P(D(x)) mean in words?
b. What does D(P(x)) mean in words?
c. Find P(D(x)) and D(P(x)).
d. As the customer, which deal is better for you?
Transcribed Image Text:4. The BestElect electronics store is having a sale on November 8th on any new electronics purchased. Every customer will receive $50 off their purchase of a new electronic item. They are also offering a student discount on every item in the store for the whole month of November. If you can prove you are a student, you will receive 15% off any item. Let x be the price of any new electronic item in the store. a. Write a function P(x) that represents the price of a new electronic item on November 8th for any customer. b. Write a function D(x) that represents the price you will pay for an item after the student discount is applied during any day in November. Now, we have two functions P and D that depend on the price of the item, x. P is a rule that says "take the price of the item, then subtract $50." D is a rule that says "take the price, then take 85% of it." If you want to take advantage of both sales, a composition of functions is necessary! But is there a difference between P(D(x)) and D(P(x))? a. What does P(D(x)) mean in words? b. What does D(P(x)) mean in words? c. Find P(D(x)) and D(P(x)). d. As the customer, which deal is better for you?
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