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Same functions return algebraically differently gives the value at a certain point for a certain form but undefined at other forms, Why is that? I can see algebraically why that's the case but intuitively I couldn't get it. could someone give me some insight or point me to the proper resource would be great.

Thanks!

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  • The last expression does not define the "same function", because it does not have the same domain as the first two. In particular, it is defined at $x=1$ whereas the other two are not. – dxiv Aug 28 '21 at 05:44
  • thanks @dxiv. but my question is why does the domain change? because we just writing the same function in a different way correct? – ARUN ARUMUGAM Aug 28 '21 at 05:48
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    thanks, @dxiv seems exactly what i need – ARUN ARUMUGAM Aug 28 '21 at 06:09

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