6 3 inverse functions l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
6.3 Inverse Functions PowerPoint Presentation
Download Presentation
6.3 Inverse Functions

Loading in 2 Seconds...

play fullscreen
1 / 5

6.3 Inverse Functions - PowerPoint PPT Presentation


  • 235 Views
  • Uploaded on

6.3 Inverse Functions. ©2001 by R. Villar All Rights Reserved. Inverse Functions. An inverse of a relation (set of ordered pairs) is obtained by switching the x and y in the ordered pairs. For example, the inverse of {(0, –3), (2, 1), (6, 3)} is: {(–3, 0), (1, 2), (3, 6)}

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '6.3 Inverse Functions' - fancy


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
6 3 inverse functions

6.3 Inverse Functions

©2001 by R. Villar

All Rights Reserved

inverse functions
Inverse Functions

An inverse of a relation (set of ordered pairs) is obtained by switching the x and y in the ordered pairs.

For example, the inverse of{(0, –3), (2, 1), (6, 3)}

is:{(–3, 0), (1, 2), (3, 6)}

The graph of the inverse is the reflection of the graph of the original relation.

The mirror of the reflection is the line y = x.

inverse

original relation

“mirror” y = x

example what is the inverse of y 3x 2
Example: What is the inverse of y = 3x – 2?

Switch the x and the y.

The inverse isx = 3y – 2

Inverses of functions are found the same way…however, the inverse of a function may or may not be a function...

For example: Find the inverse off(x) = x2. Is the inverse a function?

Replace f(x) with y y = x2

The inverse isx = y2

Graph each by making a table of values...

original function f x x 2 inverse x y 2
Original function: f(x) = x2Inverse: x = y2

y = x2

x = y2

The inverse is not a function since it does not pass the vertical line test?

y = x

composition can be used to verify if two functions are inverses of each other
Composition can be used to verify if two functions are inverses of each other...

If the functions f and g are inverses of each other, thenf(g(x)) = xand g(f(x)) = x

Example: Verify that the functions below are inverses

f(x) = 2x – 1g(x) = 1/2 x + 1/2

f(g(x)) = f(1/2 x + 1/2)

= 2(1/2 x + 1/2) – 1

= x + 1 – 1 = x

g(f(x)) = g(2x – 1)

= 1/2( 2x – 1) + 1/2

= x – 1/2 + 1/2 = x

Therefore, f and g are inverses of each other.