Download - Functions 2 inverse , composite
![Page 1: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/1.jpg)
1Ago 2806:11 p.m.
Composition of functionsInverse function
By the end of the lesson you will be able to:
• Understand and use composite functions.
• Understand and use inverse functions.
http://www.youtube.com/watch?v=GW3Sq6Ez9zA
![Page 2: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/2.jpg)
2Ago 2806:11 p.m.
Starter:
With your calculator draw the graph of y= ex.State domain, range and asymptotes of this function.
![Page 3: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/3.jpg)
3Ago 2806:11 p.m.
Composition of functions
If and
find in simplest form:
![Page 4: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/4.jpg)
4Ago 2806:11 p.m.
Given the functions andfind
![Page 5: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/5.jpg)
5Ago 2806:11 p.m.
x f(x)
f gg(f(x))
For to exist, then range of f must be included in the domain of g.
![Page 6: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/6.jpg)
6Ago 2806:11 p.m.
Indentity function:
What happens when this function is composed with another function?
g(x) = 2 x 3
=
=
![Page 7: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/7.jpg)
7Ago 2806:11 p.m.
Inverse function
x f(x)
f
f 1
The inverse of a function exists if and only if the function is a one-to-one function.
![Page 8: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/8.jpg)
8Ago 2806:11 p.m.
Which of these functions have an inverse?
![Page 9: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/9.jpg)
9Ago 2806:11 p.m.
Find the inverse of : draw the graphs of both functions. Draw the identity function on the same graph.
and
![Page 10: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/10.jpg)
10Abr 3005:32 p.m.
y = 3x+2y = x
![Page 11: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/11.jpg)
11Ago 2806:11 p.m.
The graph of is a reflection of the graph of
about the line y = x
Find the inverse function of
and sketch both graphs.
![Page 12: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/12.jpg)
12Sep 1202:30 p.m.
![Page 13: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/13.jpg)
13Ago 2806:11 p.m.
Find the inverse function of
Draw the graphs of both functions.
is a selfinverse function
![Page 14: Functions 2 inverse , composite](https://reader036.vdocument.in/reader036/viewer/2022081907/5482f066b479590a0d8b4920/html5/thumbnails/14.jpg)
14Ago 2806:11 p.m.
Find the inverse function of
for x≠1 and sketch both graphs.