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

(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

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

(g∘f)(x)=1.065x+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 find the composition of the functions \( f(x) \) and \( g(x) \).

1. The function \( g(x) \) represents the price of the cabinets plus the delivery fee: \[ g(x) = x + 150 \]

2. The function \( f(x) \) represents the cost plus tax on a purchase of \( x \) dollars: \[ f(x) = 1.065x \]

To find the total cost of the purchase (including tax and delivery), we need to apply \( f \) to the output of \( g \): \[ (f \circ g)(x) = f(g(x)) \]

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

Thus, we conclude: \[ (f \circ g)(x) = 1.065(x + 150) \]

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