Question

Find the inverse of the function below. Graph the function below and the inverse function. Determine the domain, range, and asymptotes of the function below and the inverse function. Please show all of your work. Show both graphs.
f(x)=2ln(3-x)+6

Answer 1

We don't do graphs here

Answer 2

However, the inverse is easily found:

If y = f(x), x = f^-1(y)

y = 2ln(3-x)+6
y-6 = 2ln(3-x)
(y-6)/2 = ln(3-x)
e^[(y-6)/2] = 3-x
x = 3 - e^[(y-6)/2] = f^-1(y)

So, f^-1(x) = 3 - e^[(x-6)/2]