Domain not checked out, please see inside...

[Aries]

(08-12-2015 06:44 PM)Arno K Wrote:  

(08-12-2015 04:03 PM)Aries Wrote:  You may simplify first but the fraction remains, its domain is still there, it can't be ignored ;-)

Ok, clearly the domain stays the same, but this is a removable discontinuity, usually all further calculation is then done after a sentence explaining that and then using the simplified function. Here, as I explained above its a bug in the Prime and not only there, as Tim found out.
Arno

I know the function f(x) has a "hole" that can be removed by properly "redefining" a new function F(x) in such a way it's continuous in R but it's not necessary and besides we're talking about different and separated functions, one discontinuous and the other continuous ;-)
By the way Wolfram Alpha takes only the primary f(x) into account, giving the right answer.
Discontinuity is discontinuity, what I'm interested in are the intervals where the inequality is "satisfied" and concerning to this the calculator shows the incorrect answer :-)