The cost of producing q articles is given by the function C=f(q)=100+2q.

(A) Find the formula for the inverse function.
(B) Explain in practical terms what the inverse function tells you.

I am pretty sure the answer to A is f^-1(C)=C/2-50

For B, the inverse of the function is the interchange of the dependent and indepent variable.

C = 100 + 2q

q = (100-C)/2 = 50 - C/2
The inverse function is
f^-1 (C) = 50 - (C/2)

f^-1 is the function that gives you the number of items you can produce when you input the price, C

To find the formula for the inverse function of C=f(q)=100+2q, you can follow these steps:

Step 1: Replace C with q and q with C in the equation for the original function:
q = 100 + 2C.

Step 2: Solve this equation for C. Start by subtracting 100 from both sides:
q - 100 = 2C.

Step 3: Divide both sides of the equation by 2 to isolate C:
C = (q - 100) / 2.

So, the formula for the inverse function is f^(-1)(C) = (C - 100) / 2.

Now, let's move on to explaining what the inverse function tells us in practical terms.

The inverse function of a cost function, in this case, tells you how many articles need to be produced in order to reach a certain cost. In the original function C=f(q)=100+2q, when you input a value of q (the quantity of articles produced), you get the corresponding cost of producing that quantity.

But when we use the inverse function, f^(-1)(C), and input a value of C (the cost), we get the corresponding quantity of articles that needs to be produced to achieve that cost.

For example, if you want to find out how many articles need to be produced to reach a cost of $200, you can use the inverse function:

f^(-1)(200) = (200 - 100) / 2 = 50.

This tells us that in order to reach a cost of $200, you need to produce 50 articles.

So, in summary, the inverse function allows us to determine the quantity of articles needed to achieve a given cost, whereas the original function gives us the cost associated with a given quantity of articles produced.

(A) You are correct! The formula for the inverse function of C=f(q)=100+2q is f^⁻¹(C)=C/2-50.

(B) The inverse function, f^⁻¹(q), tells us the quantity of articles that need to be produced in order to achieve a given cost. In other words, it provides a relationship between the cost and the quantity of articles produced. This information is useful for determining how many articles should be produced in order to meet cost-related goals. For example, if a company wants to minimize its cost, it can use the inverse function to find the corresponding quantity of articles that should be produced.