Answer
$f^{-1}(x)=x-4$
(the inverse is blue on the graph)
Work Step by Step
Step 1: Replace $f(x)$ with $y$.
$y=x+4$
Step 2: Interchange $x$ and $y$.
$x=y+4$
Step 3: Solve the equation for $y$.
$ x=y+4,\qquad$ ... subtract 4,
$x-4=y$
Step 4: Replace y with the notation $f^{-1}(x)$.
$f^{-1}(x)=x-4$
Graphing $f(x)=x+4,$
the y-intercept is at $(0,4)$,
the x-intercept is when $\left[\begin{array}{l}
0=x+4\\
x=-4
\end{array}\right]$, at the point (-4,0)
Plot the two points and draw a straight line through them.
Graphing $f^{-1}(x)=x-4,$
the y-intercept is at $(0,-4)$,
the x-intercept is when $\left[\begin{array}{l}
0=x-4\\
x=4
\end{array}\right]$, at the point (4,0)
Plot the two points and draw a straight line through them.
You may want to graph the line $y=x$ with a dashed line, to show the symmetry.