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Lesson 7: The inverse of a function

Topic. This lesson covers Session 7: The inverse of a function

Learning Outcomes.

• Identify one-to-one functions and understand the connection to inverse functions.
• Form connections between the definition of inverse functions, the notation of inverse functions, and the application of inverse functions.
• Find the inverse of a function graphically and algebraically.

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

1. Functions – Inverse Functions

Question of the Day: What is the opposite of ?

## Topic 1

Definition. A function is called one-to-one (or injective), if two different inputs always have different outputs .

Example. Consider the functions and , shown in the diagram below. Are either of these functions one-to-one?

Observation (Horizontal Line Test). A function is one-to-one exactly when every horizontal line intersects the graph of the function at most once.

A function is one-to-one when each output is determined by exactly one input. Therefore we can construct a new function, called the inverse function, where we reverse the roles of inputs and outputs.

Definition 7.5. Let be a function with domain and range and assume that is one-to-one. The inverse of is a function so that Example. Find the inverse of each function:

• • • VIDEO: Finding the Inverse of a Function

Video by Irania Vazquez

#### Exit Question

Find the inverse of  