Question

) Suppose you are installing a wood floor in a square room. The cost to install the floor is $9 per square foot. The area of the room is given by the function A(x) = x 2 and the cost per square foot is given by the function C(A) = 9A. Which function can be used to find the total cost to install the wood floor? A) A(C(x)) B) C(A(x)) C) x(A(C)) D) x(C(A))

Answer 1

The correct option is;

B) C(A(x))

Explanation:

The given information are;

The cost to install the floor per square foot = $9

The area of the room is given by the function A(x) = x²

The function for the cost per square foot = C(A) = 9·A

We note that the total cost to install the wood floor = (The cost to install the floor per square foot) × (The area of the room)

∴ The total cost to install the wood floor = $9 × x²

Given that A(x) = x², we have;

The total cost to install the wood floor = $9 × A(x)

Also, given that C(A) = 9·A, we have;

C(A(x)) = 9·A(x)

Therefore;

The total cost to install the wood floor in dollar amount can be given by the function, C(A(x)) = 9·A(x)