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

Question

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