To find the inverse of a function, we switch the roles of x and y and solve for y.

Given f((x+1)/2) = x + 2, let y = (x+1)/2.
Then, y = (x+1)/2
=> 2y = x+1
=> x = 2y - 1

So, the inverse function is f^-1(x) = 2x - 1

Now, to find f^-1(9), we substitute x = 9 into the inverse function:

f^-1(9) = 2(9) - 1
f^-1(9) = 18 - 1
f^-1(9) = 17

Therefore, f^-1(9) = 17.