Unit 3: Operations with & Inverse Functions (BI Chapter 5), Day 5, Inverse Functions continued

Learning Objective:

You will learn how to find inverse functions
You will learn how to verify if two functions are inverses
- Algebraically
- Graphically
- Using a table

Inverse Functions: Definition: two functions that "undo" each other are called inverse functions.

Algebraically, if you compose two functions and the result of each composition is x, the two functions are inverse functions:

and

Graphically, inverse functions are functions that are reflected across the line
In a table, you can recognize inverse functions because the x and y values are "swapped."
You can tell whether the inverse of a function will itself also be a function if it passes the Horizontal Line Test.
Given a function, to create its inverse, "Swap & Solve." Remember to follow correct order of operations!

1. Swap means replace the x-variable(s) with y, and the y with x: for example, becomes
2. Solve means solve for the "new" y. Solving the example becomes: $LaTeX: \sqrt[4]{x-10}=y$

As always, if you are struggling, be sure to check out the resources on this topic (linked below). . . and if that's not enough, come by after school for support!

Optional Homework/Practice HW #3.5: WS #2 Composition of Functions #1-25, if you need more practice with composition of functions.

Optional, but recommended: Review topics for Unit 2+3 Test (see below).

General Homework Expectations: Whether you are doing a homework assignment from the BI book, a worksheet, or some other activity, even a Desmos activity, please remember to write all the problems and show your processes in your composition (or note) book. A list of answers = no credit!

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Review Topics:

Unit 2: Rational Exponents & Radical Equations, topics include

Convert Rational Exponent to Radical Form (and Radical to Rational Exponent)
Use exponent rules with integer and rational exponents
Simplify numerical and variable expressions using rational exponents or radicals without a calculator
Rationalize denominators
Combine radical expressions using "like radicals"
Use numeracy skills to simplify expressions in context
Solve radical equations (all sorts)

Unit 3: Operations with & Inverse Functions, Topics

Adding, subtracting, multiplying, and dividing functions
Evaluating functions with operations
Composition of Functions
Evaluating Composite Functions
Exponent Rules
Number Skills

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Rational Exponents and Radical Functions Unit Resources Module

Numeracy facts you should have mastered! These basics will help you make sense of what we're doing with exponents and radicals.

Squares to 20
Cubes to 10
Powers of 2, up to $LaTeX: 2^{10}=1,024$
Powers of 3, up to
Powers of 10 (Scientific Notation)