Q. 102 - Precalculus Enhanced with Graphing Utilities

Question

Suppose that C(g) represents the cost C, in dollars, of manufacturing g cars. Explain what $C^{-1}(800,000)$ represents.

Step-by-Step Solution

Answer

$C^{-1}\left(800,000\right)$ represents the number of cars purchased in the cost $800,000$ dollars.

Step 1. Given Information

The C(g) represents the cost C, in dollars, of manufacturing g cars.

We have to explain what $C^{-1}\left(800,000\right)$ represents.

Step 2. Explanation

Let,

 $$\begin{gathered} C\left(g\right)=mg+k \\ g=\frac{C-k}{m} \end{gathered}$$

Now, interchange g and C

$C=\frac{g-k}{m}$

Thus, $C^{-1}\left(g\right) or C^{-1}\left(800,000\right)$ represents the number of cars purchased in the cost C dollars.