1. Unit 30 Functions Presentation 1 Functions, Mappings and Domains 1
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. 30.1 Functions, Mappings and Domains 1
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.
Solution 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1
Extension Question
What is the range for p?
Is this 1:1 mapping?
Yes ? ? v
(domain for p) p

4. 30.2 Functions, Mapping and Domains 2
Unit 30
30.2 Functions, Mapping and Domains 2

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

6. 30.3 Functions, Mappings and Domains 3
Unit 30
Functions, Mappings and Domains 3

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

8. Unit 30
Composite Functions

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

10. Unit 30
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
Inverse Function 2

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