1. ## Inverse Function

P(c)=-c^2+110c-2400

I need to find the inverse function.

Here's what I have done:
P=-c^2+110c-2400
P+2400=-c^2+110c
P+2400=-c(c-110)
-P-2400=c(c-110)

I know I need to solve for c, but I'm not sure what to do next...

2. ## Re: Inverse Function

I don't think you'll end up with an inverse function though...P(c) is not bijective.

3. ## Re: Inverse Function

The two values I got for c were 30 and 80. P(c) represents the daily profit earned as related to the number of cases, c, produced and sold. I have to find a function that gives the number of cases based on the profit desired. Wouldn't that be the inverse function?

4. ## Re: Inverse Function

You need to subtract P from both sides first:
0=-c^2+110c-2400-P
Now you can do the quadratic equation with a=-1, b=110, and c=-2400-P (that's c in the quadratic equation, not c the number of cases).

What richard1234 is saying is that when you write out the quadratic equation, you get two solutions (because of the + or -), and you can't have a function with two outputs for the same input. You need more information to figure out which is correct, + or -.

Sometimes in problems like this, the "-" solution ends up being physically impossible - like the number of cases being negative. I don't think that happens in your problem, though.

- Hollywood

5. ## Re: Inverse Function

Technically, since that function is not "one-to-one", it does not have an inverse. That's why you get the " $\pm$" when you solve using the quadratic formula.