Mastering Composite Functions and Their Domains

The Organic Chemistry Tutor

This comprehensive mathematics tutorial provides a deep dive into composite functions, a fundamental concept in Algebra II and Pre-Calculus. The video systematically explains how to combine two functions, f(x) and g(x), to create a new composite function. Beyond simple substitution, it tackles the often-challenging topic of determining the domain of these composite functions, emphasizing the importance of considering restrictions from both the inner input function and the final simplified expression. The instructor uses clear, step-by-step examples involving rational and radical functions to illustrate these concepts using interval notation and number lines.