Question

Brenda is building new cabinets for x dollars. The tax rate on the purchase is 6.5%. There is a delivery fee of $150, which is not taxed. The function f(x)=1.065x
represents the cost plus tax on a purchase of x dollars and the function g(x)=x+150
represents the price of the cabinets plus the delivery fee. Determine which function represents the total cost of the purchase, including tax and delivery for a purchase of x dollars?

Enter the missing values.

(1 point)
Responses

(f∘g)(x)=1.065(x+150)
open paren f circ g close paren times x is equal to 1 point 0 6 5 times open paren x plus 150 close paren

(f∘g)(x)=1.065x+150
open paren f circ g close paren times x is equal to 1 point 0 6 5 x plus 150

(g∘f)(x)=1.065x+150
open paren g circ f close paren times x is equal to 1 point 0 6 5 x plus 150

(g∘f)(x)=1.065(x+150)

Answer 1

To determine which function represents the total cost of the purchase, including tax and delivery for a purchase of \( x \) dollars, we need to analyze the functions \( f(x) \) and \( g(x) \).

1. **The function \( g(x) \)** represents the price of the cabinets plus the delivery fee. Thus, it is given by:
\[
g(x) = x + 150
\]

2. **The function \( f(x) \)** calculates the cost of the purchase plus tax. It is given by:
\[
f(x) = 1.065x
\]

Now, to find the total cost including both the delivery fee and the tax, we need to apply the tax function \( f \) to the output of the delivery function \( g \). Therefore, we need to compose the functions \( f(g(x)) \).

Calculating \( f(g(x)) \):
\[
f(g(x)) = f(x + 150)
\]

Substituting \( g(x) \) into \( f(x) \):
\[
= 1.065(x + 150)
\]

Thus, the total cost of the purchase, including tax and delivery, is represented by:
\[
(f \circ g)(x) = 1.065(x + 150)
\]

Now, from the given options, the correct representation is:
\[
(f \circ g)(x) = 1.065(x + 150)
\]

So the correct entry is:
\[
(f \circ g)(x) = 1.065(x + 150)
\]