I explained the question in the picture.
By the way, The question ask to find all continuous points. What is that mean to be continous at a point?
continuity of f at a point x means
$\displaystyle f(x)=\displaystyle{\lim_{t\to x}}f(t)$
other than using the word intensity where I think you mean density this looks correct.
There is an irrational number in any delta neighborhood of every rational no matter how small and vice versa.
So D has no limit at any of the rational or irrational numbers and thus is continuous nowhere.