Prove uniform continuity on a specific interval

Question

I have the following question:

And I'm unsure how to prove this. Firstly, I don't know how we should prove it works only on this interval. Secondly, I attempted to show |f(x) - f(y)| < epsilon, however when replacing x and y with 1/3 (As x,y >= 1/3) I get 0 obviously; this is as far as I have made it. Can someone give me some hints?

Answer 1

Hints :

1) $x,y \ge \frac 13 \Rightarrow xy \ge \frac 19$

2)$|\frac 1x - \frac 1y| = \frac {|x-y|}{|xy|}$.