Question

Real world compositions You wish to purchase an item that retails for $375. You have a $25 off coupon and a 10% off discount. What is your final sale price if you apply the coupon and then the discount at checkout?

Answer 1

In order to solve this problem using composite functions, we can define the following functions:

`\begin{gathered} f(x)=x-25 \\ \\ g(x)=0.9x \end{gathered}`

Notice that f(x) gives the sale price of a product with original cost x, after applying the coupon of 25 dollars off.

And g(x) gives the sale price of a product originally costing x, after applying a discount of 10%. When we discount 10%, the cost will be 90% of the original one: that's why we need to multiply the original cost by 90% = 0.9.

Then, since we need to first apply the coupon and then the discount, we need to find the composite function:

`(g\circ f)(x)=g(f(x))=0.9(x-25)`

Now, since the original price was $375, the final sale price will be:

`(g\circ f)(375)=0.9(375-25)=0.9(350)=315`

Therefore, the final sale price is $315.