Is the Continuity of f(x) and g(x) at x=0 and x=1/2?

[sitia]

Homework Statement

I have the function f(x) = x if x= 1/n and n is an integers / {0)
= 1- x otherwise

and the function g(x) = x if x is rational
=1- x if x is irrational

The problems is to find if the above functions are continuous at x=0 and x=1/2 each.
I am really struggling and am not sure how to go about this. Can someone help me figure it out. Please?
Thanks!

Homework Equations

The Attempt at a Solution

For x=0, I believe f(x) is not coninuous as n is an integer and so x cannot equal 0 for x=1/n
However I know that is the worng way of seeing things and I just don't know the steps to take to figuring something like this out.

 

[haruspex]

f is defined as
f(x) = x if x= 1/n for some nonzero integer n
= 1- x otherwise (i.e. for all other x)
So first question is, what is f(0)?
Next question: does f(δ) get ever closer to that value as δ approaches 0?