Question

You are buying a car whose price is $22,500. Which of the following options will you choose? Explain.

a. You are given a factory rebate of $2000, followed by a dealer discount of 10%.
b. You are given a dealer discount of 10%, followed by a factory rebate of $2000.
Let f(x) = x-2000 and let g(x) = .9x Which option is represented by the composite f(g(x))? Which option is represented by the composite g(f(x)) ?

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Answer 1

Option B

Explanation:

Option A

• 1. $22500 - $2000 = $20500
• 2. $20500 - 10% = $20500*0.9 = $18450

This is g(f(x)) since the first step is same f(x) and the second step is g(x)

Option B

• 1. $22500 - 10% = $22500*0.9 = $20250
• 2. $20250 - $2000 = $18250

This is f(g(x)) since the first step is g(x) and the second one f(x)

This option is better as 10% discount is applied to full price and final price is less.