How to Evaluate and Simplify Composite Functions

The Organic Chemistry Tutor

This educational video provides a clear, step-by-step tutorial on understanding and evaluating composite functions in algebra. The narrator distinguishes between function multiplication and function composition, using standard notation like f(g(x)) and (f o g)(x). The lesson progresses from algebraic composition, where one expression is substituted into another to create a new polynomial, to numerical evaluation, where specific values are plugged into composite functions. The content covers key algebraic skills including substitution, the distributive property, and expanding binomials (FOIL method). Two distinct examples are used: first, finding the general formulas for f(g(x)) and g(f(x)) using linear and quadratic functions; and second, evaluating specific numerical inputs for nested functions involving a cubic equation. The visual style uses digital handwriting on a black background to clearly isolate each step of the calculation. Teachers can use this video to introduce or reinforce the concept of composite functions in Algebra II or Pre-Calculus courses. It is particularly useful for clarifying the common misconception between the open circle notation for composition and the dot notation for multiplication. The step-by-step examples allow for natural pause points where students can attempt the math before seeing the solution, making it an excellent tool for guided practice.