Our objective was to enable an end-user to create complex queries to drug information sources through functional composition, by creating sequences of functions from application program interfaces (API) to drug terminologies. The development of a functional composition model seeks to link functions from two distinct APIs. An ontology was developed using Protégé to model the functions of the RxNorm and NDF-RT APIs by describing the semantics of their input and output. A set of rules were developed to define the interoperable conditions for functional composition. The operational definition of interoperability between function pairs is established by executing the rules on the ontology. We illustrate that the functional composition model supports common use cases, including checking interactions for RxNorm drugs and deploying allergy lists defined in reference to drug properties in NDF-RT. This model supports the RxMix application (http://mor.nlm.nih.gov/RxMix/), an application we developed for enabling complex queries to the RxNorm and NDF-RT APIs.