# You have a $40 coupon from the manufacturer that is good for the purchase of a cell phone. The store where you are purchasing your cell phone is offering a 40% discount on all cell phones. Let xrepresent the regular price of the cell phone. (a) Suppose only the 40% 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$40 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 ∘ g)(x)or g ∘ f)(x), depending on the order in which they are applied to the price. Find both (f ∘ g)(x) and (g ∘ f)(x).

Question

You have a $40 coupon from the manufacturer that is good for the purchase of a cell phone. The store where you are purchasing your cell phone is offering a 40% discount on all cell phones. Let xrepresent the regular price of the cell phone. (a) Suppose only the 40% 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$40 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 ∘ g)(x)or g ∘ f)(x), depending on the order in which they are applied to the price. Find both (f ∘ g)(x) and (g ∘ f)(x).