We can get the inverse function by first setting f(x) = y, solving for x, and after that switching y and x. So, let's solve for x:
[tex]f(x)= \frac{1}{2}x+4 [/tex]
[tex]y= \frac{1}{2}x+4 [/tex]
[tex]2(y-4)=x[/tex]
[tex]2x-4=y=f (x)^{-1} [/tex]
Then, just plug in 4 for x, and solve:
[tex]2(4)-4= f (x)^{-1}[/tex]
[tex]4=f (x)^{-1}[/tex]
There you have your answer.
