1. Lesson 6

1.9. Lesson 6 Summary

Mathematics 30-1 Module 7

Module 7: Rational Functions and Function Operations

 

Lesson 6 Summary

 

The first diagram shows that f composed with g can be described by applying function g to x to give g at x and then applying function f to g at x to give f at g at x. The second diagram shows that g composed with f can be described by applying function f to x to give f at x and then applying function g to f at x to give g at f at x.

 

Functions can be combined using a composition of functions. The composite function f(g(x)) can be thought of as g(x) being used as an input for f(x). The notation (f o g)(x) is often used instead of f(g(x)). Care needs to be taken when composing functions to make sure the output of the first function is a valid input into the second function.