1. Composition of functions
The composition of the function f with g is
f(g(x)) =
The domain of is the set of all x in the domain of g such that g(x) is in the domain of f.

2. Illustration of a composite function

3. Questions about composite functions
Find the inner and outer functions of the composite function on the right. Then find the domain of the inner function, the domain of the outer function and the domain of the composite function.

4. Decomposing functions
Given the two functions h(x) = f(g(x)), find the two functions
f and g
Note: there could be more than one correct answer.