Question

6. Customers at the Palace Pro Shop receive a 20% discount if they are members. All customers

must pay 7% in sales tax. The function f(x) = 0.8x is used to determine the price of an item after the

20% member discount, wherex is the regular price of the item. The function g(x) = 107x is used to

determine the total amount customers pay for a purchase after all discounts are applied. Which

function can be used to determine T(x), the total amount a member pays for an item with a regular

price of x dollars?

Answer 1

Answer: Total amount for an item would be 85.6x.

Explanation:

Since we have given that

Rate of discount = 205

Rate of sales tax = 7%

Function f(x) is used to determine the price of an item after the 20% member discount is given by

`f(x)=0.8x`

Function g(x) is used to determine the total amount customers pay for a purchase after all discounts are applied which is given by

`g(x)=107x`

we will use composite function gof(x) to find the total amount a member pays for an item with a regular price of x dollars.

`T(x)=g(f(x))=g(0.8x)=107* 0.8x=85.6x`

Hence, total amount for an item would be 85.6x.