Yep. I'm an idiot.Sorry, but the function is not defined on this range, so I don't see how it can be continuous. By defining it in the way that you have it is equivalent to the expression involving the Lambert W function that I gave in the PDF, the point of putting it in this form was to show that the function is only defined for certain values of x.

You would need to define the function differently for it to make sense over the range $\displaystyle x \in (e^{1/e},\infty)$