A store has two different coupons that customers can use. One coupon gives the customer $\$ 15$ off their purchase, and the other coupon gives the customer $40 \%$ 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 " $\$ 15$ off" coupon, and let $g$ be the function that inputs a cost (in dollars) and outputs the cost after applying the "40\% off" coupon.
Which of the following correctly represents the fact that the cost of purchasing \$360 worth of goods is \$201 when the " $40 \%$ off" coupon is applied first followed by the " $\$ 15$ off" coupon?
$f(g(360))=201$
$g(f(201))=360$
$f\left(f^{-1}(360)\right)=201$
$g(f(360))=201$
$f(g(201))=360$
Answer
Final Answer: \(\boxed{f(g(360))=201}\)
Step 1 ：The problem is asking for the correct representation of the cost of purchasing \$360 worth of goods when the '40\% off' coupon is applied first followed by the '\$15 off' coupon.
Step 2 ：The '40\% off' coupon is represented by the function g and the '\$15 off' coupon is represented by the function f.
Step 3 ：Since the '40\% off' coupon is applied first, we first input the original cost into the function g. Then, the output of g (which is the cost after the '40\% off' coupon is applied) is inputted into the function f (which represents the '\$15 off' coupon).
Step 4 ：Therefore, the correct representation is \(f(g(360))=201\).
Step 5 ：Final Answer: \(\boxed{f(g(360))=201}\)
