The question is as follows, let c=f(A) be the cost in dollars, of building a store of area A square feet. In terms of cost and square feet what do the following quantities represent?

(A) f(10,000)
(B) f^-1 (20,000)

I am pretty sure the answerfor A is C=10,000 and for part B it is f^-1(A)= 20,000

In Question A, f(20,000) is the cost (in dollars) of building a store of 20,000 square feet.

In question (B), f^-1(20,000) is the square feet of area that you can build at a cost of $20,000. The independent variable of the inverse function f^-1(C) is the cost.

Actually, the answers for the quantities (A) and (B) are slightly different. Let me explain it step by step:

(A) f(10,000):
To find the value of f(10,000), which represents the cost of building a store with an area of 10,000 square feet, we can substitute A = 10,000 into the function c = f(A) and solve for c.
So, f(10,000) represents the cost of building a store with an area of 10,000 square feet.

(B) f^(-1)(20,000):
f^(-1) represents the inverse function of f. In this case, f^(-1)(20,000) means finding the value of A when the cost of building the store is $20,000.

To determine f^(-1)(20,000), you need to solve the equation c = f(A) when c = 20,000. However, the exact equation or function f(A) needs to be provided to determine the inverse function and calculate the value of A.

Therefore, we can't determine the exact meaning of f^(-1)(20,000) without knowing the specific form of the function f(A).

To understand what the quantities (A) f(10,000) and (B) f^-1(20,000) represent in terms of cost and square feet, let's break it down:

(A) f(10,000): This expression represents the cost, in dollars, of building a store with an area of 10,000 square feet. In other words, it is calculating the value of the function f(A) when A is equal to 10,000. To find the cost, you would substitute A = 10,000 into the function f(A) and evaluate it. The result will give you the cost, in dollars, for building a store with an area of 10,000 square feet.

(B) f^-1(20,000): This expression represents the inverse function of f(A). The inverse function allows you to find the input value A that corresponds to a particular output value of 20,000. In this case, it is finding the square footage A that will result in a cost of $20,000. To find this value, you would apply the inverse function f^-1 to the cost ($20,000) and determine the corresponding square footage A.

So, the answer for (A) is the cost of building a store with an area of 10,000 square feet, and the answer for (B) is the square footage required to build a store with a cost of $20,000.