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1. Unit 30
Functions
Presentation 1 Functions, Mappings and Domains 1
Presentation 2 Functions, Mapping and Domains 2
Presentation 3 Functions, Mapping and Domains 3
Presentation 4 Composite Functions
Presentation 5 Inverse Functions 1
Presentation 6 Inverse Functions 2

2. Unit 30
30.1 Functions, Mappings and
Domains 1

3. Example
If , use the mapping diagram below to show how v
maps to p for . Consider integer values of v.
10
9
8
7
6
5
4
3
2
1
10
9
8
7
6
5
4
3
2
1
Solution
Extension Question
What is the range for p?
Is this 1:1 mapping?
Yes
?
?
v
(domain for p)
p

4. Unit 30
30.2 Functions, Mapping and
Domains 2

5. Example
Complete the mapping diagram below for the function
Consider integer values of x.
5
4
3
2
1
0
-1
-2
-3
-4
-5
25
20
15
10
5
0
Solution
Extension Questions
What is the range for y?
Is this 1:1 mapping? No ?
?

6. Unit 30
30.3 Functions, Mappings and
Domains 3

7. Example
If f is defined by; for all ,what are the values of:
(a) (b) (c) (d)
Solution
(a)
(b)
(c)
(d)
? ?
?
?
?
?
?
?
?
?
?
?
Extension Question
What is the range of f ?
Sketch the function;
?
x
y
2-2 -1 1
The function f is not
a 1:1 mapping.
Explain why not? all map to 0?

8. Unit 30
30.4 Composite Functions

9. The concept of a function of a function is introduced here.
Example
The functions of f and g are defined by
(a)Find and
(b)What are the values of and
Solution
(a) (b) ????
??
?
?
??
????

10. Unit 30
30.5 Inverse Functions 1

11. If , we can make C the subject of the equation by
writing
or
We say that F and C are inverse functions.
For inverse functions, f and g, then
Example
Show that if
then
Solution
???
?
?
Note: We write or to mean ,etc.

12. Unit 30
30.6 Inverse Function 2

13. For functions that are 1:1 mappings, we can find their inverse
functions.
Example
If , find it’s inverse function.
Solution
?
?
?
?
?
?
?
?
?
?
? ?
i.e.
Let and find x as a function of y.
Check