Question

How do you find the inverse of `f(x)=ln (3-2x)+3`?

Answer 1

Inverse is `f^-1(x) = 3/2 - (e^(x-3))/2`

Explanation:

Make `x` the subject in this equation `y= ln(3-2x) + 3`

Step 1) `y-3 = ln(3-2x)`

Step 2) Make exponential expression on both sides to get rid of `ln` so `e^(y-3) = 3-2x`

Step 3) The final form `x= 3/2 - (e^(y-3))/2`

Step 4) Final step replace x by `f^-1 (x)` and `y` by `x`.

Hope that helps,
Cheers.