1. Composition OF
Functions

2. Definition of composite functions
Suppose f and g are functions such that the range of g is the subset of the domain of f. Then the composite function
can be described by the equation

3. Let’s do an example together.
• Substitute 2x-3 in for g(x):
• Substitute into f(x):
Next

4. Simplify:

5. • Substitute for g(x):
• Substitute f(x) into g(x):
• Simplify:

6. Another example
Next

7. Try these on your own:

8. Answers:

9. Now we will go over how to find a value of composite of functions.
Find each value.
Substitute in g(x).
Substitute into g(x).
Simplify
Next

10. Substitute into f(x).
Simplify

11. Now you find the values using the same directions as in the last examples.
Answer: 64
Answer: -5