The inverse of this function is f(x) = 3x - 6.
You can find the inverse of any function by switching the f(x) and x values. Once you've done that, solve for the new f(x). The result will be the inverse function. The step-by-step process is below.
f(x) = 1/3x + 2 ---> Switch f(x) and x values
x = 1/3f(x) + 2 ---> Subtract 2 from both sides
x - 2 = 1/3f(x) ----> Multiply both sides by 3
3(x - 2) = f(x) ----> Distribute the 3
3x - 6 = f(x) ----> Place in the proper order for formatting purposes
f(x) = 3x - 6
And that is your inverse function.
