Question

Which function could be used to represent the total cost of the shoes by applying the $15 dollar coupon first and the 20% member discount second for the original cost x?

A) g(f(x))=0.8(x−15)
B) f(g(x))=0.8(x)−15
C) f(g(x))=0.2(x)−15
D) g(f(x))=0.2(x−15)

Answer 1

The total cost of the shoes after applying a $15 coupon and a 20% discount on the reduced price is represented by the function g(f(x)) = 0.8 × (x - 15), which is option A).

Step-by-step explanation:

The problem involves applying a $15 coupon to the original cost of the shoes and then applying a 20% member discount. To represent this mathematically, we define two functions: one for applying the coupon (let's call it f(x)) and another for applying the discount (g(x)). If x represents the original price, the coupon is applied first, so we have f(x) = x - 15. Then a 20% discount is applied to the new amount, which is represented by g(f(x)) = 0.8 × (f(x)). Substituting f(x) into g(f(x)), we get g(f(x)) = 0.8 × (x - 15), which is option A).