Answer
See below:
Work Step by Step
We have to evaluate the inverse of the function using the $f\left( x \right)=2x-4$ as follows:
Take $f\left( x \right)$ $=$ $y$ ,
$y=2x-4$
And interchange the variables $x$ and $y$:
And solve for $y$
$\begin{align}
& x=2y-4 \\
& x+4=2y \\
& y=\frac{x+4}{2}
\end{align}$
Replace $y$ with ${{f}^{-1}}\left( x \right)$ ,
${{f}^{-1}}\left( x \right)=\frac{x+4}{2}$.
Let us draw the graph as follows:
Steps 1:
The $x\text{-intercepts}$ and $y\text{-intercepts}$ are
$\left( 4,0 \right)$ And $\left( 0,2 \right)$.
And for the inverse function:
The intercepts are $\left( -4,0 \right)$ and $\left( 0,2 \right)$.
Step 2:
Plot the intercepts and join the intercepts in the graph.
The graph of the functions $f\left( x \right)=2x-4$ and ${{f}^{-1}}\left( x \right)=\frac{x+4}{2}$ in the rectangular coordinate system is:
The graph of the functions $f\left( x \right)=2x-4$ and ${{f}^{-1}}\left( x \right)=\frac{x+4}{2}$ intersects the x-axis at the points $\left( 2,0 \right)$ and $\left( -4,0 \right)$, respectively.
