How to Find the Domain of Composite Functions

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step guide on how to determine the domain of composite functions, a key concept in precalculus and algebra. Through the use of specific examples involving rational and radical functions, the narrator demonstrates that finding the domain isn't as simple as just looking at the final simplified equation. The video uses a logical "input-output" approach, comparing functions to a cooking process where inputs must be compatible with each stage of preparation. The content progresses from a numerical investigation using a table of values to an analytical algebraic method. It highlights the two main sources of domain restrictions: values excluded from the inner function, and values that cause the inner function to output a number that is undefined in the outer function. This dual-layer analysis is crucial for students who often miss the second type of restriction. Teachers can use this video to introduce or reinforce the complex topic of composite domains. It breaks down the process into four actionable steps: finding the inner domain, finding the outer domain, solving for x-values that violate the outer domain, and combining the results. The visual aids and pause points make it an excellent tool for interactive classroom learning or flipped classroom assignments.