Proving Convergence of f_n(a_n) to f(a) Given Uniform Convergence of f_n on I

[Treadstone 71]

"Suppose f_n are defined and continuous on an interval I. Assume that f_n converges uniformly to f on I. If a_n in I is a sequence and a_n -> a, prove that f_n(a_n) converges to f(a)."

I don't understand the question. Doesn't uniform convergence imply that for all x in I and e>0, | f_n(x) - f(x) | < e? So in particular, |f_n(a_n) - f(a) | < e.

 

[Treadstone 71]

Wait, nevermind. | f_n(a_n) - f(a_n) | <e, not f(a).