Answer
(a) $f^{-1}(x)=x-2$
(b) See the image below.
Work Step by Step
(a) To find inverse of the function $f(x)=2+x$, we have to write it down in terms of $y$ and $x$ and then replace them by each other. And at last solve for $y$. So we have: $y=2+x$
Inverse: $x=2+y$
$y=x-2$
$f{-1}(x)=x-2$
(b) We can graph them using graphing calculator, or even simply take two arbitrary $x$ value to find corresponding $y$ value and graph it by connecting these points.
See the image above.