Answer
(a) $f^{-1}(x)=-2x+4$
(b) See the image below.
Work Step by Step
(a) To find inverse of the function we have to follow the next strategy:
First write down the function in terms of $y$ and $x$,
Then replace $y$ by $x$ and vice versa,
At last solve the equation for $y$.
We have $f(x)=2-\frac{1}{2}x$
$y=2-\frac{1}{2}x$
$x=2-\frac{1}{2}y$
$\frac{1}{2}y=2-x$
$y=2(2-x)$
$y=4-2x$
$f^{-1}(x)=-2x+4$
(b) We can sketch the graph of these functions using graphing calculator. See the image above.