Inverse Functions: Index

I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on the different definitions on inverse functions that appear in Precalculus and Calculus.

Square Roots, nth Roots, and Rational Exponents

Part 1: Simplifying \sqrt{x^2}

Part 2: The difference between \sqrt{t} and solving x^2 = t

Part 3: Definition of an inverse function and the horizontal line test

Part 4: Why extraneous solutions may occur when solving algebra problems involving a square root

Part 5: Defining \sqrt{x}

Part 6: Consequences of the definition of \sqrt{x}: simplifying \sqrt{x^2}

Part 7: Defining \sqrt[n]{x} if n is odd or even

Part 8: Rational exponents if the denominator of the exponent is odd or even

Arcsine

Part 9: There are infinitely many solutions to \sin x = 0.8

Part 10: Defining arcsine with domain [-\pi/2,\pi/2]

Part 11: Pedagogical thoughts on teaching arcsine.

Part 12: Solving SSA triangles: impossible case

Part 13: Solving SSA triangles: one way of getting a unique solution

Part 14: Solving SSA triangles: another way of getting a unique solution

Part 15: Solving SSA triangles: continuation of Part 14

Part 16: Solving SSA triangles: ambiguous case of two solutions

Part 17: Summary of rules for solving SSA triangles

Arccosine

Part 18: Definition for arccosine with domain [0,\pi]

Part 19: The Law of Cosines and solving SSS triangles

Part 20: Identifying impossible triangles with the Law of Cosines

Part 21: The Law of Cosines provides an unambiguous angle, unlike the Law of Sines

Part 22: Finding the angle between two vectors

Part 23: A proof for why the formula in Part 22 works

Arctangent

 

Part 18: Definition for arctangent with domain (-\pi/2,\pi/2)

Part 24: Finding the angle between two lines

Part 25: A proof for why the formula in Part 24 works.

Arcsecant

Part 26: Defining arcsecant using [0,\pi/2) \cup (\pi/2,\pi]

Part 27: Issues that arise in calculus using the domain [0,\pi/2) \cup (\pi/2,\pi]

Part 28: More issues that arise in calculus using the domain [0,\pi/2) \cup (\pi/2,\pi]

Part 29: Defining arcsecant using [0,\pi/2) \cup [pi,3\pi/2)

Logarithm

Part 30: Logarithms and complex numbers

 

 

 

Leave a comment

4 Comments

  1. 100,000 page views | Mean Green Math
  2. My Favorite One-Liners: Part 9 | Mean Green Math
  3. My Favorite One-Liners: Part 11 | Mean Green Math
  4. My Favorite One-Liners: Part 63 | Mean Green Math

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: