This lecture covers the continuity of the reciprocal function, focusing on the criteria for a strictly monotone function to be injective. It explains the relationship between the function and its reciprocal, emphasizing the conditions for continuity and injectivity. The instructor also highlights the properties of bijective functions and the concept of reciprocal functions. The lecture concludes with a reminder about the continuity of a reciprocal function for a bijective continuous function over a given interval.