Answer
$f^{-1}(x)=\dfrac{x}{4}-2.25$
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:
$y=4x+9$
Interchange $x$ and $y$ then solve for $y$ to have:
$x = 4y+9
\\x-9= 4y
\\\dfrac{x-9}{4}=y
\\\dfrac{x}{4} -\dfrac{9}{4}=y
\\y=\dfrac{x}{4} -2.25$
Replace $y$ with $f^{-1}(x)$ to have:
$f^{-1}(x)=\dfrac{x}{4} -2.25$
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).
