  In this paper, we extend the investigations regarding Birkhoff-James
orthogonality of linear operators to bounded continuous functions on metric
spaces. We introduce Birkhoff-James extensions of continuous functions and
study them in detail, in the separate contexts of compact and non-compact
metric spaces. We conclude by discussing an application of our ideas to the
study of Birkhoff-James orthogonality in $C(X)$ with the supremum norm, where
$X$ is a compact metric space.
