Lesson 4: Composite Function
(1) The meaning of "composite?
A composite function is made up of several functions in a sequential order. For example gf represents a composite function whereby function f is applied first followed by function g.
(2) Existence of composite function
A composite function exists if the range of the first function is a subset of the domain of the second function.
E.g. The composite function gf exists if .
(3) Domain & Rule of composite function gf
(4) Range of composite function gf
Sketch the graph of gf (x) under the domain of gf (= domain of f) and obtained the range from the set of y values from the graph.
Method 2 (mapping method):
Sketch the graph of the second function, g under the domain given by the range of the first function. Then the range of the composite is the set of y values from the graph.
Given two functions f and g defined as follows:
Show that the composite gf exists and find its domain, rule and range.