Function Composition and Inverse Functions: Algebraic Foundations

A strong grasp of functions is essential for success in advanced mathematics, computer science, and data analysis. This course provides the rigorous algebraic framework needed to understand how functions map inputs to outputs and how they can be combined or reversed. By the end of this course, you will possess a solid algebraic understanding of function notation, identifying domain and range restrictions, and executing function composition and simple inverse derivations. You will gain confidence in manipulating complex algebraic expressions systematically. What you'll learn: * Define and interpret function notation, domain, and range for linear, polynomial, and rational function types. * Practice the algebraic manipulation required to perform function composition (f(g(x)) and g(f(x))). * Understand the necessary conditions, including the horizontal line test, for a function to possess a true inverse. * Apply algebraic steps to derive the inverse function for simple linear and quadratic expressions. * Analyze function mapping to identify domain restrictions that impact composition and the existence of inverses. The course begins with core definitions and terminology before moving into practical algebraic techniques for combining functions. We emphasize clear, step-by-step methods for solving problems and checking results using written exercises. This course is designed for absolute beginners in advanced algebra, pre-calculus, or anyone needing to refresh their foundational knowledge of functions before tackling more complex mathematical or programming concepts. No prior knowledge of calculus or advanced mathematics is required. Start building your essential algebraic skills today.