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A discount store’s prices are 25% lower than department store prices. The function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars.

If the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. The function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars.

Create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month.

d(c(x)) =

We have been given that a discount store’s prices are 25% lower than department store prices. The function [tex]c(x)=0.75x[/tex] represents the cost (c), in dollars, of an item, where x is the department store price, in dollars.

We are also told that when the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. The function [tex]d(y)=0.85y-5[/tex] represents d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars.

We are supposed to find the function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month.

We can see that function d(c(x)) is a composite function. To get our composite function we just need to substitute function c(x) in function d(y).

After making the substitution we will get our desired function as,

[tex]d(c(x))=0.80*(0.75x)-5[/tex]

Upon simplifying our function will be:

[tex]d(c(x))=0.60x-5[/tex]

Therefore, the function [tex]d(c(x))=0.60x-5[/tex] represents the final price of an item when a costumer buys an item that has been in the discount store for a month.