First, replace f(x) by y. This is done to make the rest of the process easier.
Now, replace every x with y and a every y with an x:
Now, solve this equation for y. Then, we must move -8 to the left hand side as +8. It yields
Now, we can apply logarithms in both sides:
For the properties of logarithms, we have
then, we have
and we obtain
Finally, replace y with f^1. Then, the inverse funcion is
The graphs of the function and its inverse are: