Question

A clothing store is having a clearance sale. all coats are 20% off, and then an additional $10 is taken off the sale price of each. a 7% sales tax is then added. the following functions represent each part of the transaction. sales price: f(x) = 0.8x additional amount off: g(x) = x – 10 final price: h(x) = 1.07x which is the composed function for the total price, x, of any item?

a) h(g(f(x))) = 1.07x – 10
b) h(g(f(x))) = 1.07(0.8x – 10)
c) h(g(f(x))) = 0.8x – 1.07
d) h(g(f(x))) = 1.07(0.8x – 10x)

Answer 1

The composed function for the total price, x, of any item is h(g(f(x))) = 1.07(0.8x – 10).

Step-by-step explanation:

The composed function for the total price, x, of any item is option b) h(g(f(x))) = 1.07(0.8x – 10). To find the total price, we need to follow the order of operations and simplify the composed function step by step.

1. Start with the sales price function, f(x) = 0.8x, which represents the initial price of the item with the 20% discount.
2. Then apply the additional amount off function, g(x) = x – 10, which subtracts $10 from the sale price.
3. Finally, apply the final price function, h(x) = 1.07x, which adds a 7% sales tax to the price after the discount and additional amount off.

When we compose these functions together, we get h(g(f(x))) = 1.07(0.8x – 10). This represents the total price of any item after the discount, additional amount off, and sales tax have been applied.