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This lecture covers algebraic operations on functions, focusing on even and odd functions defined on a symmetric domain. It discusses the properties of even and odd functions under addition, multiplication, and composition, providing examples of even functions like cos(x) + x² and odd functions like sin(x) + x. Additionally, it explores periodic functions, highlighting their properties and the behavior of their sum and product. The lecture concludes with a detailed analysis of the periodicity of functions and the implications of their periods on the sum of functions.