Tutorials--Function Inverses
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This document provides 18 examples exploring the concept of functions and their inverses. It examines linear, quadratic, exponential, logarithmic, cubic, quartic and radical functions. Students are shown how the graph of y=x serves as the axis of reflection for determining a function's inverse, and that the inverse of a function is not always a function itself.
Tutorials--Function Inverses
- 1. Functions and Their Inverses
- 2. 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.
- 3. Functions and Their Inverses: Example 1. Find the inverse of a linear function in slope-intercept form with a positive slope and b > 0.
- 4. Functions and Their Inverses: Example 2. Find the inverse of a linear function in slope-intercept form with a positive slope and b < 0.
- 5. Functions and Their Inverses: Example 3. Find the inverse of a linear function in slope-intercept form with a negative slope and b > 0.
- 6. Functions and Their Inverses: Example 4. Find the inverse of a linear function in slope-intercept form with a negative slope and b < 0.
- 7. Functions and Their Inverses: Example 5. Find the inverse of a quadratic function in standard form, where a > 0, c > 0.
- 8. Functions and Their Inverses: Example 6. Find the inverse of a quadratic function in standard form, where a < 0, c > 0.
- 9. Functions and Their Inverses: Example 7. Find the inverse of a quadratic function in standard form, where a > 0, c < 0.
- 10. Functions and Their Inverses: Example 8. Find the inverse of a quadratic function in standard form, where a < 0, c < 0.
- 11. Functions and Their Inverses: Example 9. Find the inverse of an exponential function with base 2.
- 12. Functions and Their Inverses: Example 10. Find the inverse of an exponential function with base 10.
- 13. Functions and Their Inverses: Example 11. Find the inverse of an exponential function with base e.
- 14. Functions and Their Inverses: Example 12. Find the inverse of a logarithmic function with base 2.
- 15. Functions and Their Inverses: Example 13. Find the inverse of a logarithmic function with base 10.
- 16. Functions and Their Inverses: Example 14. Find the inverse of a logarithmic function with base e.
- 17. Functions and Their Inverses: Example 15. Find the inverse of a cubic function.
- 18. Functions and Their Inverses: Example 16. Find the inverse of a quartic function.
- 19. Functions and Their Inverses: Example 17. Find the inverse of a radical function of root 2.
- 20. Functions and Their Inverses: Example 18. Find the inverse of a radical function of root 3.