Problema Solution
At a picture frame shop you order a $29 picture frame. You have a $20 gift certificate and a 17% discount coupon. The picture frame shop allows you to use both discounts at once, and gives you the option of which discount is taken first. Use composition of the following functions to make your decision. In which order should you take the discounts to obtain the lowest price?
d(x) = x - 20.00
p(x) = 0.83x
Answer provided by our tutors
d(p(x) = 0.83x - 20.00
for x = $29 we have d(p(29) = 0.83*29 - 20.00 = $4.07
p(d(x)) = 0.83(x - 20.00)
for x = $29 we have p(d(29)) = 0.83(29 - 20.00) = $7.47
since $4.07 < $7.47 you should first use the 17% discount coupon and then use the $20 gift certificate.