1. COMBINING FUNCTIONS

2. SOME FUNCTION RULES : SUM DIFFERENCE PRODUCT QUOTIENT COMBINING FUNCTIONS

3. EXAMPLE # 1 : Find

4. COMBINING FUNCTIONS EXAMPLE # 1 : Find

5. COMBINING FUNCTIONS EXAMPLE # 1 : Find EXAMPLE # 2 : Find

6. COMBINING FUNCTIONS EXAMPLE # 1 : Find EXAMPLE # 2 : Find

7. COMBINING FUNCTIONS EXAMPLE # 3 : Find

8. COMBINING FUNCTIONS EXAMPLE # 3 : Find EXAMPLE # 4 : Find

9. COMBINING FUNCTIONS COMPOSITE FUNCTIONS :

10. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : EXAMPLE : Find

11. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : EXAMPLE : Find

12. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : EXAMPLE # 2 : Find

13. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : EXAMPLE #2 : Find

14. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : EXAMPLE # 3 : Find

15. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : EXAMPLE # 3 : Find

16. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : In some cases, we will be given the composite function and we will need to find the two functions that created that composite function.

17. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : In some cases, we will be given the composite function and we will need to find the two functions that created that composite function. In most cases, look for expressions inside parentheses and also expressions under roots. However, this is not always the way to attack these problems.

18. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : In some cases, we will be given the composite function and we will need to find the two functions that created that composite function. In most cases, look for expressions inside parentheses and also expressions under roots. However, this is not always the way to attack these problems. EXAMPLE : is the result of a composite function Find f(x) and g(x).

19. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : In some cases, we will be given the composite function and we will need to find the two functions that created that composite function. In most cases, look for expressions inside parentheses and also expressions under roots. However, this is not always the way to attack these problems. EXAMPLE : is the result of a composite function Find f(x) and g(x). Think ; I have “something” raised to the third power. The “something” is g(x), raised to the third power

20. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : In some cases, we will be given the composite function and we will need to find the two functions that created that composite function. In most cases, look for expressions inside parentheses and also expressions under roots. However, this is not always the way to attack these problems. EXAMPLE : is the result of a composite function Find f(x) and g(x). Think ; I have “something” raised to the third power. The “something” is g(x), raised to the third power

21. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : In some cases, we will be given the composite function and we will need to find the two functions that created that composite function. In most cases, look for expressions inside parentheses and also expressions under roots. However, this is not always the way to attack these problems. EXAMPLE : is the result of a composite function Find f(x) and g(x).

22. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : In some cases, we will be given the composite function and we will need to find the two functions that created that composite function. In most cases, look for expressions inside parentheses and also expressions under roots. However, this is not always the way to attack these problems. EXAMPLE : is the result of a composite function Find f(x) and g(x). Think ; I have the square root of“something”. The “something” is g(x), under a square root

23. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : In some cases, we will be given the composite function and we will need to find the two functions that created that composite function. In most cases, look for expressions inside parentheses and also expressions under roots. However, this is not always the way to attack these problems. EXAMPLE : is the result of a composite function Find f(x) and g(x). Think ; I have the square root of“something”. The “something” is g(x), under a square root

24. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : When determining the domain of composite functions, it is necessary to look at domain values individually as well as the composite.

25. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : When determining the domain of composite functions, it is necessary to look at domain values individually as well as the composite. EXAMPLE :

26. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : When determining the domain of composite functions, it is necessary to look at domain values individually as well as the composite. EXAMPLE : The domian of ƒ(x) is all real numbers except zero…

27. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : EXAMPLE : When determining the domain of composite functions, it is necessary to look at domain values individually as well as the composite. The domian of ƒ(x) is all real numbers except zero… Performing the composite …

28. COMBINING FUNCTIONS COMPOSITE FUNCTIONS : EXAMPLE : Domain – all real numbers except x = 0, - 3 Performing the composite … The domian of ƒ(x) is all real numbers except zero… When determining the domain of composite functions, it is necessary to look at domain values individually as well as the composite.