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Question 983509: Hello, I really need some help on this problem I was assigned. It's pretty challenging.. Thank you in advance!
You have a $50 coupon from the
manufacturer good for the purchase of a cell phone. The store
where you are purchasing your cell phone is offering a 20%
discount on all cell phones. Let x represent the regular price of
the cell phone.
(a) Suppose only the 20% discount applies. Find a function f
that models the purchase price of the cell phone as a function of the regular price x
(b) Suppose only the $50 coupon applies. Find a function g
that models the purchase price of the cell phone as a function
of the sticker price x.
(c) If you can use the coupon and the discount, then the purchase
price is either (f o g)x or (g o f)x , depending on the
order in which they are applied to the price. Find both (f o g)x and (g o f)x . Which composition gives the lower price?
Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website! Let x = regular price of the cell phone.
(a) Suppose only the 20% discount applies.
.
f(x)=0.8x
.
(b) Suppose only the $50 coupon applies.
.
g(x)=x-$50
.
(c) If you can use the coupon and the discount, then the purchase
price is either (f o g)x or (g o f)x. Which composition gives the lower price?
.
f(g(x))=0.8(x-$50)
g(f(x))=0.8x-$50 This is the lower price.
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