Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Functions and Graphs
Subtopic: Composite and Inverse Functions

Overview

Although this material is all review from intermediate algebra, it is important in this course to make firm your understanding of the material and expand it to college level concepts. These ideas and processes form the basis for our work with various special functions in the remainder of this course.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 2.4.1 Understand and use properly the mathematical notation for composite functions and for inverse functions
• 2.4.2 Evaluate composition of functions (given equations, list of ordered pairs, or graphs)
• 2.4.3 Determine if a relation is one-to-one (given a list of ordered pairs, graph, or equation)
• 2.4.4 Inverse functions: determine if f^-1 exists, find f^-1 algebraically, verify f^-1 algebraically

Terminology

Terms you should be able to define: composite function, inverse function, one-to-one, horizontal line test

Mini-Lectures and Examples

Supplemental Resources

Use my Functions and Graphs Checklist as a checklist to be sure that you have learned all that you should Patrick Just Math Tutorial's Inverse Functions - The Basics is a comprehensive (rather long) video with a good variety of algebraic processes related to inverse functions. You may find useful Prof. Wlodarczyk's Overview of Functions which presents definitions and examples, many with graphs. The Math Page's Topics in Precalculus: Inverse Functions provides an overall review of inverse functions. PurpleMath's Inverse Functions provides complete coverage of inverse functions from Intermediate Algebra and College Algebra courses.

rev. 2020-10-10