Question

A clothing store is having a sale in which customers can receive 30% off their purchase and $10 off using a coupon. The function f(x) = 0.7x represents the price after a 30% discount and the function g(x) = x − 10 represents the price after a $10 discount. Which of the following is the function f(g(x)) and what does it represent? (1 point)

f(g(x)) = 0.7x − 7 represents the purchase price after a $10 discount and then 30% off the remaining amount
f(g(x)) = 0.7x − 10 represents the purchase price after a 30% discount and then $10 off the remaining amount
f(g(x)) = 0.7x − 3 represents the purchase price after a $10 discount and then 30% off the remaining amount
f(g(x)) = 0.3x − 10 represents the purchase price after a 30% discount and then $10 off the remaining amount

Answer 1

f(g(x)) = 0.7x - 7 represents the purchase price after a $10 discount and then 30% off the remaining amount.

Explanation:

The function f(x) = 0.7x represents the price after a 30% discount and the function g(x) = x − 10 represents the price after a $10 discount. To find f(g(x)), we substitute g(x) into f(x) for x, giving:

f(g(x)) = 0.7(g(x)) = 0.7(x - 10)

= 0.7x - 7

Therefore, the function f(g(x)) = 0.7x - 7 represents the purchase price after a $10 discount and then 30% off the remaining amount.