Chapter 4.7, Problem 42HP

To determine

To prove: The two functions are inverse by graphing the functions and line $y=x$ .

Explanation of Solution

Step-1

Consider $f(x)=2x-1$ is the function.

Find the inverse of function. First substitute y for f(x) and exchange x and y with each other.

  $\begin{array}{l}f(x)=2x-1\\ y=2x-1\\ x=2y-1\end{array}$

Now, solve for y.

  $\begin{array}{l}x+1=2y\\ \frac{x+1}{2}=y\end{array}$

Substitute $f^{-1}(x)$ for y.

  $f^{-1}(x)=\frac{x+1}{2}$

This is the required inverse function.

Graph:

  

Graph in which red line show the function line and blue line show the inverse of function line and green line show the line $y=x$ .