Question

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

Answer 1

`f^(-1)(y)=(3-e^(y-3))/2`

Explanation:

Let `y=f(x)` then `x=f^(-1)(y)` and `y=ln(3-2x)+3`
Rewrite as `ln(3-2x)=y-3`
Taking exponents gives `3-2x=e^(y-3)`
This gives `x=f^(-1)(y)=(3-e^(y-3))/2`