Given a metric space (X, dx), let C(X) denote the set of continuous functions from X to $\displaystyle R$. For two functions $\displaystyle f, g$ in C(X), define

d($\displaystyle f,g$) = sup |$\displaystyle f(x) - g(x)$| for x in X.

Prove that C(X) is path-connected.

Thanks!