Let x represent the original price of the computer

Question

You have a coupon for $200 off the price of a computer.When you arrive, you find that the computers are on sale for 20% off. Let x represent the original price of the computer,

a. Use function notation to describe the cost f(x), using only the coupon.

 

b. Use function notation to describe the cost g(x), with only the 20% discount.

 

c. Form the composition of the functions f and g that represents the cost if you use the coupon first and then take the 20% discount.

 

d. Form the composition of the functions f and g that represents the cost if you use the discount first and then use the coupon. 

 

e. Would you pay less for the computer if you used the coupon first or took the 20% discount first? Explain your reasoning. Provide examples to support your answer.

 

Answer 1

 

a)

 

When you have a coupon, it means you pay less for what it is worth on the price tag, thus saving you money.  Since the coupon is $200 off the original price, we just subtract the coupon value from the price on the tag.

 

f(x) = x - 200

 

 

b)

 

When we have a discount, we are paying less than price on the tag.  This is similar to a coupon.  Since we have 20% off the original price, we multiply the price on the tag by 0.20. Then subtract that resulting amount from the original price. 

 

g(x) = x - 0.20x

 

 

c)

 

(g o f)(x) = g(f(x))

 

 

d)

 

(f o g)(x) = f(g(x))

 

 

e)

 

Select a reasonable value of x.  Since the coupon is $200 off the original price, let x = 500.

 

Substitute that value into the answers from parts c and d.  Compare their resulting prices.