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- Oct 22nd 2009, 10:27 PMbinkypoohow can I prove if this function is continuous or not!
- Oct 22nd 2009, 10:34 PMredsoxfan325
- Oct 25th 2009, 08:05 PMbinkypoo
doesnt this show that f is continuous at x = 0? What about the rest of the domain?

- Oct 25th 2009, 08:19 PMredsoxfan325
It's continuous everywhere else because and are. The composition of continuous functions is continuous.

- Oct 25th 2009, 08:33 PMbinkypoo
I guess my problem is I dont know how to show that and 1/x are continuous EVERYWHERE. Could you explain that please? thanks

- Oct 25th 2009, 08:54 PMredsoxfan325
I don't think your professor expects you to do all that, but if he does, you need to crank out the - proofs for each one.

For let , because

For , you can probably Google a proof. The idea is to let and then use a difference-to-product identity to convert into something more manageable.

is kind of a pain in the ass, and I've screwed up continuity proofs of this function before. There are probably other threads on MHF with proofs of this.