Inverse, Exponential and Logarithmic Functions Chapter 11 Inverse, Exponential and Logarithmic Functions
11.1 Inverse Functions
Find the equation of the inverse of a function. 11.1 Inverse Functions Objectives Decide whether a function is one-to-one and, if it is, find its inverse. Use the horizontal line test to determine whether a function is one-to-one. Find the equation of the inverse of a function. Graph f –1 from the graph of f. Copyright © 2010 Pearson Education, Inc. All rights reserved.
11.1 Inverse Functions Functions Revisited 5 8 –3 11 2 1 3 1 2 –1 3 4 2 1 3 Domain Range 1 2 –1 3 4 Domain Range Copyright © 2010 Pearson Education, Inc. All rights reserved.
11.1 Inverse Functions Functions Revisited 5 1 –3 8 3 11 2 Domain Range 5 1 –3 8 3 11 2 This is a function. Copyright © 2010 Pearson Education, Inc. All rights reserved.
11.1 Inverse Functions Functions Revisited 1 3 2 4 –1 Domain Range 1 3 2 4 –1 This is not a function. Copyright © 2010 Pearson Education, Inc. All rights reserved.
11.1 Inverse Functions One-to-One Functions 5 1 3 1 –3 2 8 3 4 11 2 –1 Domain Range Domain Range 5 1 3 1 –3 2 8 3 4 11 2 –1 is one-to-one is not one-to-one Copyright © 2010 Pearson Education, Inc. All rights reserved.
Relationship Between One-to-One and Inverse 11.1 Inverse Functions Relationship Between One-to-One and Inverse . Copyright © 2010 Pearson Education, Inc. All rights reserved.
Relationship Between One-to-One and Inverse 11.1 Inverse Functions Relationship Between One-to-One and Inverse . Copyright © 2010 Pearson Education, Inc. All rights reserved.
Horizontal Line Test and One-to-One Functions 11.1 Inverse Functions Horizontal Line Test and One-to-One Functions . Copyright © 2010 Pearson Education, Inc. All rights reserved.
Horizontal Line Test and One-to-One Functions 11.1 Inverse Functions Horizontal Line Test and One-to-One Functions . Copyright © 2010 Pearson Education, Inc. All rights reserved.
Finding the Equation of the Inverse of a Function 11.1 Inverse Functions Finding the Equation of the Inverse of a Function Copyright © 2010 Pearson Education, Inc. All rights reserved.
Finding the Equation of the Inverse of a Function 11.1 Inverse Functions Finding the Equation of the Inverse of a Function Copyright © 2010 Pearson Education, Inc. All rights reserved.
Finding the Equation of the Inverse of a Function 11.1 Inverse Functions Finding the Equation of the Inverse of a Function Copyright © 2010 Pearson Education, Inc. All rights reserved.
Finding the Equation of the Inverse of a Function 11.1 Inverse Functions Finding the Equation of the Inverse of a Function Copyright © 2010 Pearson Education, Inc. All rights reserved.
Finding the Equation of the Inverse of a Function 11.1 Inverse Functions Finding the Equation of the Inverse of a Function Solve for y. Copyright © 2010 Pearson Education, Inc. All rights reserved.
Graphing f –1 from the Graph of f 11.1 Inverse Functions Graphing f –1 from the Graph of f Copyright © 2010 Pearson Education, Inc. All rights reserved.
Graphing f –1 from the Graph of f 11.1 Inverse Functions Graphing f –1 from the Graph of f Copyright © 2010 Pearson Education, Inc. All rights reserved.
Graphing f –1 from the Graph of f 11.1 Inverse Functions Graphing f –1 from the Graph of f These pairs of points are mirror images with respect to y = x. Copyright © 2010 Pearson Education, Inc. All rights reserved.