What is the domain of the function ? The answer is because if or a divide by zero situation occurs. One is sorely tempted to simplify to which would be incorrect as it stands since now needs to be explicitly stated. So .
Wolfram Alpha handles this function curiously. If the original functions is input as , Alpha simplifies it to with nary a mention that . This is clearly wrong. Alpha also shows the graph of the function as if exists instead of displaying a hole.
If the expression is entered, Alpha still simplifies it to and shows a function plot without a hole at . However in a box entitled “Properties as a real function” the domain is correct. I have alluded to problems with Wolfram Alpha in this post and this post.