Composite Functions

written like f(g(x)) or (f∘g)(x) the ∘ between f and g is the composition symbol function inside another function g(x) is the inner function f(x) is the outer function

Input Process for Evaluation

in the function f(g(x))

How to find Domain

1. Identify domain restrictions of the inner function
2. Find composite function
3. Identify domain restrictions of composite function
4. Find domain includes both restrictions DOMAIN FOR $fog\ne gof$

Function and its inverse

Graphing $f^{-1}(f(x))$ will turn out to be y=x, WITH RESTRICTIONS. restrictions depend on the 2 functions

$(fog{)}^{-}1=(g^{-1}o{f}^{-1})$