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.
