AllBestEssays.com - All Best Essays, Term Papers and Book Report
Search

Nazi Era

Essay by   •  November 28, 2017  •  Term Paper  •  1,187 Words (5 Pages)  •  936 Views

Essay Preview: Nazi Era

Report this essay
Page 1 of 5

6.2        One to One Functions; Inverse Functions        p. 411

[pic 1]

In other words, a function is a one to one function if each -value corresponds to only one -value and each -value corresponds to only one -value.[pic 2][pic 3][pic 4][pic 5]

Are the following functions one-to-one?

                                                                 [pic 6][pic 7]

D  1  2  3  4                                                 D   1   2   3   4   5[pic 8][pic 9][pic 10][pic 11][pic 12][pic 13][pic 14][pic 15][pic 16][pic 17]

R  2  4  7  10                                                R   2   4   4  10  6[pic 18]

A way to show that a function is not one to one is to produce a pair of different domain elements () that lead to the same function () value.[pic 19][pic 20]

Decide whether the following are one to one?

a)                                  b[pic 21][pic 22]

c)                                                  d)  [pic 23][pic 24]

[pic 25]

[pic 26][pic 27]

In general, a function that is either increasing or decreasing over its entire domain will be one to one.

Inverse Functions

 = {(-1, 1), (1, 3), (2, 5)}                        Is this one to one?[pic 28]

 = {(1, -1), (3, 1), (5, 2)}                        Is this one to one?[pic 29]

What do you notice about the domain and range of these two functions?

A function has an inverse if you can reverse the domain and range and the resulting relation is a function.

Dog                       Weight                                        Weight             Dog[pic 30][pic 31][pic 32][pic 33]

Indiana                95[pic 34]

Archer                72[pic 35][pic 36][pic 37]

Buster                 56[pic 38]

                                                                        [pic 39][pic 40]

  Brian                Mary[pic 41][pic 42][pic 43][pic 44]

  Jeff                Mary[pic 45][pic 46]

Stephanie        Mary[pic 47][pic 48][pic 49]

[pic 50]

A special notation is used for inverse functions:  If  is the inverse of a function , then is written as -1 (read as “-inverse”. [pic 51][pic 52][pic 53][pic 54][pic 55]

If  is a one to one function. Then  is the inverse of    if [pic 56][pic 57][pic 58]

...

...

Download as:   txt (3.5 Kb)   pdf (371.8 Kb)   docx (185.9 Kb)  
Continue for 4 more pages »
Only available on AllBestEssays.com
Citation Generator

(2017, 11). Nazi Era. AllBestEssays.com. Retrieved 11, 2017, from https://www.allbestessays.com/essay/Nazi-Era/68331.html

"Nazi Era" AllBestEssays.com. 11 2017. 2017. 11 2017 <https://www.allbestessays.com/essay/Nazi-Era/68331.html>.

"Nazi Era." AllBestEssays.com. AllBestEssays.com, 11 2017. Web. 11 2017. <https://www.allbestessays.com/essay/Nazi-Era/68331.html>.

"Nazi Era." AllBestEssays.com. 11, 2017. Accessed 11, 2017. https://www.allbestessays.com/essay/Nazi-Era/68331.html.