Find the domain of f(x).

Then find the inverse of the function, and the domain of the inverse.

I know how to find the domain and inverse, but I just have no idea how to do it in this function.

For domain, I'm guess 3 - e^2x > or = 0

-e^2x > or = -3

e^2x < or = 3

2x < or = ln3

x < or = ln3 / 2

Is that right? Something just doesn't feel right.

EDIT: K, nvm. That first part was right.

But I didn't get the inverse right.

x^2=3-e^2y

x^2 - 3 = -e^2y

ln(x^2 - 3) = -2y

-ln(x^2 - 3) / 2 = y