Nazi Era
Essay by lmaobit • November 28, 2017 • Term Paper • 1,187 Words (5 Pages) • 1,051 Views
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]
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