textbook-theory · English
General Composition of Functions
A three-page mathematics lecture note introducing the concept of function composition, defining g∘f as the combined action of applying f then g to a real-valued input. The document covers composition notation and examples using polynomial, trigonometric, and power functions, then reframes stretches and shifts of functions as special cases of composition. It concludes with techniques for decomposing complex functions into simpler compositions, motivating the chain rule for differentiation.
function compositionmathematicsstretches and shiftschain rule