Question

Find the inverse function of

f(x) = 1.5 ln(x-2) + 4

Please help! I don't even know where to start ):

Answer 1

The inverse function gives you back x when you input f(x)

Let y = f(x) = 1.5 ln(x-2) +4
(y-4)/1.5 = ln (x-2)
e^[(y-4)/1.5) = x-2
x = e^[(y-4)/1.5) + 2

Now switch variables for the inverse function

f^(-1)(x) = e^[(x-4)/1.5) + 2