This paper addresses the relationship between Mathematical Works Space (MWS) and Mathematics Teacher's Specialized Knowledge (MTSK) models through the analysis of lessons episodes where the function concept is treated, particularly the calculation of pre images. In these episodes elements that allow a complementary analysis are identified from both frames, enabling a deepening understanding of knowledge of the mathematics teacher as a common actor in both models. We conclude with a summary of the common elements found between subdomains of MTSK and the MWS components.