Question

A store has two different coupons that customers can use. One coupon gives the customer $35 off their purchase, and the other coupon gives the customer 35% off of their purchase. Suppose they let a customer use both coupons and choose which coupon gets applied first. For this context, ignore sales tax.
Let f be the function that inputs a cost in dollars) and outputs the cost after applying the "$35 off" coupon, and let g be the function that inputs a cost in dollars) and outputs the cost after applying the "30% off" coupon.

Required:
What is correctly represents the fact that the cost of purchasing $190 worth of goods is $98 when the "30% oft" coupon is applied first followed by the "$35 off" coupon?

Answer 1

Answer:

h(x)=f[g(x)]=0.7x-35

Step-by-step explanation:

In this case function f, which inputs a cost and outputs the cost after applying the $35 off coupon looks like this:

f(x)=x-35

where x is the cost of the purchase. In this case we are subtracting the $35 from the cost x.

Function g, which inputs a cost and outputs the cost after applying the 30% off coupon looks like this:

g(x)=x-0.3x

g(x)=0.7x

in this case we are subtracting 30 percent of the cost from the cost of the purchase.

So in order to find a function that represents the cost of the purchase when first applying the 30% coupon and then the $35 coupon we will need to get a composite function f(g(x)). Which means we need to substitute function g(x) into the f(x) function so we get:

h(x)=f[g(x)]=(0.7x)-35

or:

h(x)=0.7x-35

We can prove this function works when plugging x=$190 in so we get:

h(190)=0.7(190)-35

h(190)=133-35

h(190)=98