Identities of Lambert W Function

Hi, I was recently viewing a Wikipedia article on Lambert W Function. I was going through the identities and found this identity:

It says that it is true of all x>= than -1/e. I typed this identity in WolframAlpha and inserted a value of -2/e, which is outside the given domain. And here is what I got

It says that it is true? How?!!

Also, another identity:

According to my observation, the given domain should be 0<=a<=e