The inverse of this function is f(x) = 2x - 12.
You can find the inverse of any function by switching the f(x) and x values in the equation. Then you can solve for the new f(x) value. The result is your inverse function. The work for this one is below.
f(x) = 1/2x + 6 ----> switch f(x) and x
x = 1/2f(x) + 6 ----> subtract 6
x - 6 = 1/2f(x) ----> multiply by 2
2x - 12 = f(x) ----> change the order for consistency.
f(x) = 2x - 12