A website is having a sale of 15 percent off the price, x , of regular-priced items. For its loyalty club members, the site is offering an additional 15 percent off the sale price. An 8 percent shipping and handling fee is then added to the discounted price to determine the final cost. The given functions represent each part of a loyalty member’s purchase. Sales price: cap s times x is equal to 0 point 8 5 x Loyalty member discount: cap l times cap s is equal to 0 point 8 5 cap s Final cost: cap c times cap l is equal to 1 point 0 8 liters Which is the composite function for the price a loyalty member would pay based on the original price, x ?
Answer
A
cap c times open paren cap l times x close paren is equal to 2 point 7 8 0 0 x
B
cap c times open paren cap l times x close paren is equal to 0 point 9 1 8 0 x
C
cap c times open paren cap l times x close paren is equal to 0 point 7 2 2 5 x
D
cap c times open paren cap l times x close paren is equal to 0 point 7 8 0 3 x
Explanation
Apply each function in order: the sale price is 0.85x, and the additional loyalty discount makes it 0.85(0.85x) = 0.7225x. Adding the 8% shipping fee multiplies that amount by 1.08, giving 1.08(0.7225x) = 0.7803x. The composite function is 0.7803x, choice D.
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