Hi guys, I've been trying to do this for a while but I'm not really getting anywhere. Hints would be much appreciated!

**The problem**

Prove that the function

is continuous on

, but cannot be defined at the origin

in such a way that the resulting function is continuous on

.

**My attempt**

Just the first part for now - proving continuity on

.

They want an

proof. Here we go...

Let

.

Let

.

Then

and

we have:

Now I take the case where

is such that

and we have...

So it's proven for such

(I think?)

Now I have no idea what to do about

such that

. Or was splitting it into two cases a bad idea? Am I going anywhere useful here?

Please help!