Answer
$f^{-1}(x)=-2x+4$
(the inverse is blue on the graph)
Work Step by Step
Step 1: Replace $f(x)$ with $y$.
$y=-\displaystyle \frac{1}{2}x+2$
Step 2: Interchange $x$ and $y$.
$x=-\displaystyle \frac{1}{2}y+2$
Step 3: Solve the equation for $y$.
$ x=-\displaystyle \frac{1}{2}y+2,\qquad$ ... add $-2$,
$ x-2=-\displaystyle \frac{1}{2}y,\qquad$ ... multiply with $(-2)$
$-2x+4=y$
Step 4: Replace y with the notation $f^{-1}(x)$.
$f^{-1}(x)=-2x+4$
Graphing $f(x)=\displaystyle \frac{1}{2}x-1, \left[\begin{array}{lll}
x & f(x) & (x,y)\\
0 & 2 & (0,2)\\
4 & 0 & (4,0)
\end{array}\right], $
the graph of $f(x)$ is a line passing through $(0,2)$ and $(4,0)$.
The graph of $f^{-1}(x)$ is a line passing through points (y,x) of the above table,
$(2,0)$ and $(0,4)$.
