Chapter 1.9, Problem 100E

(a)

To determine

Determine the each function with its graph.

Answer to Problem 100E

It is very clear that line $n$ is reflection of $m$ over line $y=x$ .

Explanation of Solution

Given:

The cost $C\left(x\right)=7.50x+1500$

The cost $C$ for a business to make personalized T-shirts is given by $C\left(x\right)=7.50x+1500$ .

Graph of $C$ and $C^{-1}$ are shown below:

  

Comparing the equation $C\left(x\right)=7.50x+1500$ by $y=mx+b$ , the slope is $7.50x$ and $y$ intercept is $\left(0,1500\right)$ . Therefore, the line m shows the graph of $C\left(x\right)=7.50x+1500$ .

From the above graph it is very clear that line $n$ is reflection of $m$ over line $y=x$ .

Hence line $n$ shows its inverse $C^{-1}$ .

(b)

To determine

Find what $C\left(x\right)$ and $C^{-1}\left(x\right)$ represent in the context of the problem.

Answer to Problem 100E

  $C\left(x\right)$ representthe number of t-shirts when the cost of business is given

and

  $C^{-1}\left(x\right)$ represent the cost of business when number of t-shirt is given.

Explanation of Solution

Given:

The cost $C\left(x\right)=7.50x+1500$

The $C\left(x\right)=7.50x+1500$ represents gives the number of t-shirts when the cost of business is given. And it's inverse gives the cost of business when number of t-shirt is given.