Hello,
You're right, the functions satisfying for all are continuous on . In fact they are even differentiable on . Can you show it ?
So far, I have this:
Proving is continuous:
Need to show: .
Therefore:
Let
Hence so continuity is proved.
However, i'm sure this helps but I can't see why. I've also tried expanding the right and left hand sides but that doesn't help either.
Does anyone have any hints?