Chapter 3: Functions and Graphs 3.6: Inverse Functions

1. Chapter 3: Functions and Graphs3.6: Inverse Functions Essential Question: How do we algebraically determine the inverse of a function

2. 3-6: Inverse Functions • To invert a function, switch x and y values. • That is, if a point (a, b) is on the graph of f, then the point (b, a) is on the graph of the inverse. • Example: Write a table that represents the inverse of the function given by the table.

3. 3-6: Inverse Functions • To invert a function algebraically, swap x and y values, then try to solve the equation for y. • Example • y = 3x – 2

4. 3-6: Inverse Functions • Example • f(x) = x2 + 4x • y = x2 + 4x

5. 3-6: Inverse Functions • You can determine if a graph is a function by using the vertical line test • A graph is considered one-to-one, if it’s inverse is also a function • You can determine a graph is one-to-one by using a horizontal line test

6. 3-6: Inverse Functions • Determine if the following graphs are one-to-one • f(x) = 7x5 + 3x4 – 2x3 + 2x + 1 • g(x) = x3 – 3x – 1 Yes, the graph is one-to-one No, the graph is not one-to-one

7. 3-6: Inverse Functions • Assignment • Page 212 – 213 • Problems: 1, 9 – 19 (odd), 23 – 29 (odd)