COMPOSITE FUNCTIONS I
PAGE 1 OF 5, WHAT IS f(g(x))? INSIDE THEN OUTSIDE
COMPOSITE
TWO FUNCTIONS, ONE PIPELINE
A composite function applies one function to the output of another. We write f(g(x)) and read it "f of g of x." Think of x entering machine g first; whatever comes out becomes the input to machine f. The whole combined rule is a new function. We also write (f ∘ g)(x) = f(g(x)), where the small circle means composition (not multiplication). The key habit: work inside out: always evaluate the inner function g before the outer function f.
⚡ DEFINITION
(f ∘ g)(x) = f(g(x)). Inner function g runs first; outer function f acts on the result. Read "f composed with g."
FLOW!
INSIDE
g(x) runs first
📥 Inner function
✅ e.g. g(3) before f
📥 Inner function
✅ e.g. g(3) before f
OUTSIDE
f(input) runs second
📤 Outer function
✅ f acts on g(x)
📤 Outer function
✅ f acts on g(x)