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.

Illustration of a composite function

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.

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.