About This Chapter
Understanding Inverse Functions - Chapter Summary
If you need help understanding inverse functions in math, this chapter can help. Containing simple and engaging video and text-based lessons, the chapter helps you define and understand the inverses of logarithmic and trigonometric functions. You'll also review the steps that are needed to calculate derivatives of inverse trig functions. By the end of the chapter, you'll be able to:
- Interpret inverse functions
- Write the inverse of logarithmic functions
- Identify inverse trigonometric function properties
- Calculate derivatives and integrals of inverse trigonometric functions
To help you practice solving inverse function problems on your own, we've included self-assessment quizzes throughout the chapter. If you have any questions about the lesson topics, you can reach out to our expert math instructors. Print the lesson transcripts to supplement your studying experience. The chapter is also available to access at any time that fits your schedule.
1. Inverse Functions
Inverse functions are two functions that do exactly opposite things. Check out this lesson to learn about how to write inverse functions, find inverse functions, and predict whether or not they exist.
2. Writing the Inverse of Logarithmic Functions
Watch this video lesson to learn how inverses are related to the original function. Also learn a method to find the inverse of logarithmic functions that you can easily use.
3. Properties of Inverse Trigonometric Functions
After watching this video lesson, you will understand why our inverse trigonometric functions have a limited range. Learn what this does. Also learn the notation for these functions.
4. How to Calculate Derivatives of Inverse Trigonometric Functions
Like a metronome, trigonometric functions are regular. Even predictable. In this lesson, you will learn how to use this predictability to remember the derivative formulas for these common functions.
5. Integrals of Inverse Trigonometric Functions
With the general formulas for the derivatives of inverse trigonometric functions, we can use integration by parts with substitutions to derive the corresponding formulas for their integrals.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards