what is the inverse function of f(x)= 3 + 8x/9

To find the inverse of a function, Do as follows:

Let y = 3 + \frac{8x}{9}

Make x the subject of formula;

You'll have y-3 = \frac{8x}{9}

9(y-3) =8x

\frac{9(y-3)}{8} =x

Now, replace your y by x and x by f inverse.

f^{-1}(x) = \frac{9(x-3)}{8}

Here it is, your inverse function! :)