Answer
$f^{-1}(x)=\dfrac{x}{2} + 1.5$
Refer to the attached image below for the graph of the given function (red) and its inverse (green).
Work Step by Step
Replace $f(x)$ by $y$ to have:
$y=2x-3$
Interchange $x$ and $y$ then solve for $y$ to have:
$x = 2y-3
\\x+3= 2y
\\\dfrac{x+3}{2}=y
\\\dfrac{x}{2} + 1.5=y
\\y=\dfrac{x}{2} + 1.5$
Replace $y$ with $f^{-1}(x)$ to have:
$f^{-1}(x)=\dfrac{x}{2} + 1.5$
Create a table of values for each function (refer to attached image below)
Then, plot each ordered pair and connect them using a line to complete the graph (refer to the attached image in the answer part to see the graph).
