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Chapter 5: Q. 75 (page 258)

Discounts The manufacturer of a computer is offering two discounts on last year鈥檚 model computer. The first discount is a $200 rebate and the second discount is 20% off the regular price, p.

(a) Write a function f that represents the sale price if only the rebate applies.

(b) Write a function g that represents the sale price if only the 20% discount applies.

(c) Find f鈭�gand g鈭�f. What does each of these functions represent? Which combination of discounts represents a better deal for the consumer? Why?

Short Answer

Expert verified

(a)fp=p-200

(b)gp=0.8p

(c)f鈭�g=0.8p-200andg鈭�f=0.8p-160

Step by step solution

01

Step 1. Given Information

The manufacturer of a computer is offering two discounts on last year鈥檚 model computer. The first discount is a $200 rebate and the second discount is 20% off the regular price, p.

02

Part (a) Step 1. Finding a function f that represents the sale price if only the rebate applies.

Let p=regular price of the computer

The rebate offered is$200..Thus, the function that will represent the sale price if the rebate$200 is applied is one where is subtracted from the regular price of the computer, that

is:

fp=p-200

03

Part (b) Step 1. A function g that represents the sale price if 20% discount applies

The function that represents the sale price if only the 20%discount is one where 20% is taken off the regular price of the computer.

gp=100-20%pgp=80%p

04

Part (c) Step 1. Finding f∘g

f鈭�g=fgp=f0.8pf鈭�g=0.8p-200

05

Part (c) Step 2. Finding g∘f

g鈭�f=gfx=gfpg鈭�f=gp-200g鈭�f=0.8p-200g鈭�f=0.8p-160

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