View by Category

Loading...

PPT – Inverse Functions PowerPoint presentation | free to view - id: 11e3bb-NmZlM

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Inverse Functions

NOTE f-1 (x) does NOT mean 1/f(x)

Inverse Functions

- Example Verify that f(x)-3x6 and g(x)-1/3x2

are inverses - Solution Find f(g(x)) and g(f(x)). If they

both equal x, then they are inverses.

g(f(x)) -1/3(-3x6)2 x-22 x

f(g(x)) -3(-1/3x2)6 x-66 x

ONE-TO-ONE FUNCTIONS

A function is one-to-one if for each y-value

there is only one x-value that can be paired with

it that is, no two ordered pairs have the same

second component.

Horizontal Line Test

- Used to determine whether a functions inverse

will be a function by seeing if the original

function passes the horizontal line test. - If the original function passes the horizontal

line test, then its inverse is a function. - If the original function does not pass the

horizontal line test, then its inverse is not a

function.

Finding the Inverse of a function

- The inverse of a function f can be found as

follows - Replace f (x) with y.
- Interchange x and y.
- Solve the resulting equation for y. If this

equation does not define y as a function of x,

the function does not have an inverse. Or

equivalently, the function is f is not a

one-to-one function and has no inverse - If f has an inverse, replace y in step 3 with f

-1 (x).

Sine Function Cosine Function

Inverse Trig Functions

- Goals
- Understand Domain/Range requirements for inverse

trig functions - Be able to calculate exact values for inverse

trig functions - Understand the composition of inverse trig

functions

The Inverse Sine Function

- The inverse sine function, also called the

arcsine function, is denoted by sin-1 or arcsin. - The function sin-1 has domain -1,1 and range

-p/2, p / 2 - In other words, y arcsin x, iff sin y x

The Inverse Cosine Function

- The inverse cosine function, also called the

arccosine function, is denoted by cos-1 or

arccos. - The function cos-1 has domain -1,1 and range

0, p - In other words, if y arccos x, iff cos y x

The Inverse Tangent Function

- The inverse tan function, also called the arctan

function, is denoted by tan-1 or arctan. - The function tan-1 has domain of all real numbers

and range -p/2 y p/2 - In other words, y arctan x, iff tan y x

tan (tan -1 x ) x for real numbers

tan -1(tan x ) x -p/2 x p/2

Summary

- With no restrictions, inverses of sin, cos and

tangent are not functions. - With restrictions
- Arcsin(x) ?
- Domain x-1 x 1
- Range? -p/2 ? p/2
- Arccos(x) ?
- Domain x-1 x 1
- Range ?0 ? p
- Arctan(x) ?
- Domain xx ? R
- Range ? -p/2 ? p/2

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Inverse Functions" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Gpc University and other schools with their online training by sharing educational presentations for free