Question

For what value(s) of x is g continuous?
f(x) =

0 if x is rational
5x if x is irrational

Answer 1

this seems like an incomplete question, I'm not quite sure what it is asking.

Answer 2

Go through the epsilon-delta description if you want full marks but just draw a graph if you want to work out the answer intuitively. All irrational numbers lie on the line y=5x. All rational number on y=0. The only place this formula could be continuous is at x=0 wherer they cross (and it is).