Does there exist a function f 0 infinity rightarrow R such

Does there exist a function f : (0, infinity) rightarrow R such that lim_x rightarrow p f (x) = infinity for all positive rational numbers p?

Solution

yes

we have given at all posible rational numbers function value apporch to infinte

but at all irrational numbe fucntion can be a real value

Such function can be exist