1. ## Inverse f(x)

Well. I have to figure out the inverse function of a particular function.

That function being ln|x-2| + 3.

I got it to x-3 = ln|y-2|, but how do I get y on it's own? I imagine it has some to do with e^x considering it's ln|x|'s inverse.

Well I think I've got it now to be e^(x-3) + 2

2. Originally Posted by StephenPoco
Well. I have to figure out the inverse function of a particular function.

That function being ln|x-2| + 3.

I got it to x-3 = ln|y-2|, but how do I get y on it's own? I imagine it has some to do with e^x considering it's ln|x|'s inverse.

Well I think I've got it now to be e^(x-3) + 2
Are you sure you not given an interval in the question?
This function is not one-to-one function.

3. Originally Posted by StephenPoco
Well. I have to figure out the inverse function of a particular function.

That function being ln|x-2| + 3.

I got it to x-3 = ln|y-2|, but how do I get y on it's own? I imagine it has some to do with e^x considering it's ln|x|'s inverse.

Well I think I've got it now to be e^(x-3) + 2 and x > 2
That's only half of the truth ...

1. I assume that the function is

$\displaystyle f(x)=\left\{\begin{array}{rcl}\ln(x-2)+3&~if~&x>2 \\ \ln(2-x)+3&~if~&x<2 \end{array}\right.$

2. Each "branch" of f is a one-to-one function. Therefore you have to calculate 2 different inverses.