Hi everyone! Read through the material below, watch the videos, and follow up with your instructor if you have questions.

Lesson 6: Operations on functions

Topic. This lesson covers Session 6: Operations on functions

Learning Outcomes.

• Compute and simplify the sum, difference, product and quotient of functions.
• Compute and simplify the composition of functions.

WeBWorK. There is 1 WeBWorK assignment on today’s material:

1. Functions – Operations

Question of the Day: If we add two functions together, is the result a function?

## Operations on functions

We can make new functions by combining functions in various ways — these include the usual operations (addition, subtraction, multiplication, division) and an important new idea called composition.

Example 6.1. Let and . Find the following functions, and state their domain. Example 6.3. Let and let Find the functions and and state their domains.

VIDEO: Examples – Operations on Functions

Video by Irania Vazquez

#### Composition of functions

The composition of functions describes what happens when we put an input into an initial function , and then we plug the output of into another function — it is like plugging a value into two functions in a row

Definition. Let and be functions, and assume that is in the domain of Then define the composition of and at to be Example. Let and Find the following compositions
a) b) c) d) VIDEO: Example – Composition of functions

Video by Irania Vazquez

#### Exit Question

Given the functions and , find and simplify the compositions and . and .