Can Continuity at 0 Guarantee Equality at 0?

[mathmajor2013]

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).

Homework Equations

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

The Attempt at a Solution

NO CLUE. My intuition says false.

 

[tiny-tim]

hi mathmajor2013!

hint: forget lim x->0 …

what is lim n->0 ? ​

 

[HallsofIvy]

I'm wondering if tiny-tim didn't mean "$n\to \infty$"?

 

[tiny-tim]

oops!