Functions and Their Inverses

Overview

 This set of tutorials provides 18 examples that explore the concept of functions and their inverses. We look at both linear and non-linear functions.

Through these examples, students should get a clear illustration of the role of the graph of y = x as the axis of reflection for functions and their inverses. Students should also note that the inverse of a function isn’t always itself a function.

Functions and Their Inverses: Example 1. Find the inverse of a linear function in slope-intercept form with a positive slope and b > 0.

Functions and Their Inverses: Example 2. Find the inverse of a linear function in slope-intercept form with a positive slope and b < 0.

Functions and Their Inverses: Example 3. Find the inverse of a linear function in slope-intercept form with a negative slope and b > 0.

Functions and Their Inverses: Example 4. Find the inverse of a linear function in slope-intercept form with a negative slope and b < 0.

Functions and Their Inverses: Example 5. Find the inverse of a quadratic function in standard form, where a > 0, c > 0.

Functions and Their Inverses: Example 6. Find the inverse of a quadratic function in standard form, where a < 0, c > 0.

Functions and Their Inverses: Example 7. Find the inverse of a quadratic function in standard form, where a > 0, c < 0.

Functions and Their Inverses: Example 8. Find the inverse of a quadratic function in standard form, where a < 0, c < 0.

Functions and Their Inverses: Example 9. Find the inverse of an exponential function with base 2.

Functions and Their Inverses: Example 10. Find the inverse of an exponential function with base 10.

Functions and Their Inverses: Example 11. Find the inverse of an exponential function with base e.

Functions and Their Inverses: Example 12. Find the inverse of a logarithmic function with base 2.

Functions and Their Inverses: Example 13. Find the inverse of a logarithmic function with base 10.

Functions and Their Inverses: Example 14. Find the inverse of a logarithmic function with base e.

Functions and Their Inverses: Example 15. Find the inverse of a cubic function.

Functions and Their Inverses: Example 16. Find the inverse of a quartic function.

Functions and Their Inverses: Example 17. Find the inverse of a radical function of root 2.

Functions and Their Inverses: Example 18. Find the inverse of a radical function of root 3.