1. COMPOSITION OF
FUNCTIONS
“SUBSTITUTING ONE FUNCTION INTO ANOTHER”

2. Must be able to work either
The Composition Function
Must be able to work either
This is read “f composition g” and means to copy the f function down but where ever you see an x, substitute in the g function.
FOIL first and then distribute the 2

3. You could multiply this out but since it’s to the 3rd power we won’t
This is read “g composition f” and means to copy the g function down but where ever you see an x, substitute in the f function.
You could multiply this out but since it’s to the 3rd power we won’t

4. This is read “f composition f” and means to copy the f function down but where ever you see an x, substitute in the f function. (So sub the function into itself).

5. A MathXTC Example of Composite Functions
Try it !!

6. Method 1

7. Method 1

8. Method 1

9. Method 2

10. Method 2

11. Acknowledgement
I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint.
Shawna has kindly given permission for this resource to be downloaded from and for it to be modified to suit the Western Australian Mathematics Curriculum.
Stephen Corcoran
Head of Mathematics
St Stephen’s School – Carramar