Chapter 1.6, Problem 126E

(a)

To determine

The inverse function of $y=12+0.55x$ .

Answer to Problem 126E

The inverse function of $y=12+0.55x$ is $f^{-1}(x)=\frac{x-12}{0.55}$ .

Explanation of Solution

Given data:

Function: $y=12+0.55x$

Calculation:

The inverse function of $y=12+0.55x$ :

  $\begin{array}{l}y=12+0.55x\\ y-12=0.55x\\ x=\frac{y-12}{0.55}\\ f^{-1}(x)=\frac{x-12}{0.55}\end{array}$

The number of unit produced f-1(x) in terms of hourly wage x

Conclusion:

The inverse function of $y=12+0.55x$ is $f^{-1}(x)=\frac{x-12}{0.55}$ .

(b)

To determine

To graph: The inverse function of $y=12+0.55x$ .

Explanation of Solution

Given information:

Function: $y=12+0.55x$

Graph:

The graph of equation $y=12+0.55x$

and its inverse function:

  

Interpretation:

The inverse function is reflection of the original function.

(c)

To determine

To find: Hourly wage when 9 units were used.

Answer to Problem 126E

Hourly wage when 9 units used are $16.95.

Explanation of Solution

Given data:

Function: $y=12+0.55x$

Calculation:

Hourly wage when 9 units are used:

  $\begin{array}{l}y=12+0.55x\\ y=12+0.55(9)\\ y=16.95\$\end{array}$

Conclusion:

Hourly wage when 9 units used are $16.95

(d)

To determine

To find: Units used when hourly wage is $21.35.

Answer to Problem 126E

17 units used when hourly wage is $21.35.

Explanation of Solution

Given data:

Function: $y=12+0.55x$

Calculation:

Number of units when hourly wage is $21.35:

  $\begin{array}{l}{f}^{-1}(x)=\frac{x-12}{0.55}\\ f^{-1}(x)=\frac{21.35-12}{0.55}\\ f^{-1}(x)=17units\end{array}$

Conclusion:

17 units used when hourly wage is $21.35: