Answer
The graph is shown below:
Work Step by Step
We have to plot the graph of $ f\left( x \right)=2x-4$; replace $ f\left( x \right)$ and substitute y in place of $ f\left( x \right)$; then evaluate the value of the y variable for each value of the x variable or the value of the x variable for each value of the y variable.
To find the value of the y-intercept, substitute $ x=0$ as given below:
$\begin{align}
& y=2x-4 \\
& =2\left( 0 \right)-4 \\
& =0-4 \\
& =-4
\end{align}$
To find the value of the x-intercept, substitute $ y=0$ as given below:
$\begin{align}
& y=2x-4 \\
& 0=2x-4 \\
& 2x=4 \\
& x=2
\end{align}$
Therefore, plot the intercepts $\left( 0,-4 \right)\text{ and }\left( 2,0 \right)$ and draw a line passing through these points to get the graph of equation $ f\left( x \right)=2x-4$.
To compute the value of ${{f}^{-1}}$, rewrite the equation $ y=2x-4$ in terms of $ x $:
$\begin{align}
& y=2x-4 \\
& 2x=y+4 \\
& x=\frac{y+4}{2}
\end{align}$
Now, put x in place of y and ${{f}^{-1}}$ in place of x:
${{f}^{-1}}=\frac{x+4}{2}$
Also, in order to plot the graph of ${{f}^{-1}}=\frac{x+4}{2}$, put y in place of ${{f}^{-1}}$ and evaluate the value of the y variable for each value of the x variable:
To find the value of the y-intercept, substitute $ x=0$ as given below:
$\begin{align}
& y=\frac{x+4}{2} \\
& y=\frac{0+4}{2} \\
& =\frac{4}{2} \\
& =2
\end{align}$
To find the value of the x-intercept, substitute $ y=0$ as given below:
$\begin{align}
& y=\frac{x+4}{2} \\
& 0=\frac{x+4}{2} \\
& x+4=0 \\
& x=-4
\end{align}$
Therefore, plot the intercepts $\left( 0,2 \right)\text{ and }\left( -4,0 \right)$ and draw a line passing through these points to get the graph of the equation ${{f}^{-1}}=\frac{x+4}{2}$.
