*
*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.

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Different yet, you could as Wolfram|Alpha for the domain of the function:

http://www.wolframalpha.com/input/?i=what+is+the+domain+of+1%2F%28%28x-3%29%2F%28x-4%29%29%3F

This time it answers correctly with a line graph of the domain.