Question

The cost of producing q newspaper articles is given by the function C = f(q) = 100 + 2q. a.) Find a formula for the inverse function. b.) Explain in practical terms what the inverse function tells you.

Answer 1

a.)
`f^(-1) (q) =(C - 100)/(2)`

b.) The inverse function allows me to understand the number of newspapers articles I can produce using different amounts of money to spend on production costs.

Step-by-step explanation:

Finding the inverse function

The cost of production function is the mathematical formula that tells how much cost is required to produce certain amount of newspaper articles. The invere function then is the one that tell us the reversed concept: how many newspapers article you can produce if you have certain amount of money for production. How do we get the inverse function? As the function is solved for C (cost of production), we need now to solve it for q (quantity of newspapers articles). This process is as follows:

1. 
   `C = 100 + 2q` (That is the cost function)
2. Substract 100 from the function:
   `C - 100 = 2q`
3. Divide by 2:
   `(c - 100)/(2) = q`
4. Reorganizing:
   `q = (C - 100)/(2)`

That is okay, but what does it mean to us?

The inverse function would at first glance seem to mean the same than the original function but said in other way, but this function it is very useful by itself. Let's think about this case: If you are the head of the printing house and you have a limited budget to produce the articles. How do you know you have enough money to produce the number of articles for all your readers in the city? Just replace C for your budget and see if the amount of articles will be enough. Just as simple as replacing values. Mathematics at service of printing houses.