True or False? Continuity Problem: f(0)=g(0)

[mathmajor2013]

1. Homework Statement

True or false? If f and g are continuous at 0 and f(1/(2n+7))=g(1/(7-2n)) for all positive integers n, then f(0)=g(0).

2. Homework Equations

lim x->0 f(x)=f(0)
lim x->0 g(x)=g(0)

3. The Attempt at a Solution

NO CLUE. My intuition says false.

 

[l'Hôpital]

What is the definition of continuity at 0?

What happens as n--> infinity?