IntroFoundations
Composition of Functions
Overview
f(g(x)) means: apply g first, then feed the result into f. Composition is everywhere in calculus — the Chain Rule is built entirely on it.
Key Concepts
1
(f ∘ g)(x) = f(g(x)) — g runs first, f runs second
2
Order matters: f(g(x)) ≠ g(f(x)) in general
3
Identify the "outer" function f and the "inner" function g
4
This exact decomposition is what the Chain Rule uses
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