Given:

f(x)= X^2 ---------for all rational x

= -X --------for all irrational x

Prove that it is continous at x=0 and discontinous at every point.

I've proved for continous part (with epsilon-delata language). But couldn't do the discontinous part. Tried contradiction, but am getting nothing out of it. If anyone can do it rigorously, it would be highly appreciated.

Thanks