COMBINING FUNCTIONS

SOME FUNCTION RULES :

SUM

DIFFERENCE

PRODUCT

QUOTIENT

xgxfxgf

xgxfxgf

xgxfxgf

xgxf

xg

f

COMBINING FUNCTIONS

COMBINING FUNCTIONS

EXAMPLE # 1 : Find

2 and 62 xxgxxxf

3gf

COMBINING FUNCTIONS

EXAMPLE # 1 : Find

2 and 62 xxgxxxf

3gf

716

1639

23633

3332

gfgf

COMBINING FUNCTIONS

EXAMPLE # 1 : Find

2 and 62 xxgxxxf

3gf

716

1639

23633

3332

gfgf

EXAMPLE # 2 : Find 1 gf

COMBINING FUNCTIONS

EXAMPLE # 1 : Find

2 and 62 xxgxxxf

3gf

716

1639

23633

3332

gfgf

EXAMPLE # 2 : Find 1 gf

336

3611

21611

1112

gfgf

COMBINING FUNCTIONS

EXAMPLE # 3 : Find

2 and 62 xxgxxxf

1fg

414

1611

21611

1112

gffg

COMBINING FUNCTIONS

EXAMPLE # 3 : Find

2 and 62 xxgxxxf

1fg

414

1611

21611

1112

gffg

EXAMPLE # 4 : Find 0

g

f

3

2

6

20

600

0

0 2

g

f

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xfgxfg

xgfxgf

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xfgxfg

xgfxgf

xxgxxf 2 and 32

1

EXAMPLE : Find 6gf

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xfgxfg

xgfxgf

xxgxxf 2 and 32

1

EXAMPLE : Find

532342

14

4626

66

f

g

gfgf

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xfgxfg

xgfxgf

xxgxxf 2 and 32

1

EXAMPLE # 2 : Find 6fg

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xfgxfg

xgfxgf

xxgxxf 2 and 32

1

EXAMPLE #2 : Find

2020

033362

16

66

g

f

fgfg

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xfgxfg

xgfxgf

xxgxxf 2 and 32

1

EXAMPLE # 3 : Find agf

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xfgxfg

xgfxgf

xxgxxf 2 and 32

1

EXAMPLE # 3 : Find

22

12

32

1132

2

12

2

aaf

aaaf

aag

agfagf

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xgfxgfxh

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

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xgfxgfxh

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.

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xgfxgfxh

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 32 xxh

Find f(x) and g(x).

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xgfxgfxh

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 32 xxh

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

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xgfxgfxh

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 32 xxh

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

3)(

2)(

xxf

xxg

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xgfxgfxh

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 32 xxh

Find f(x) and g(x).

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xgfxgfxh

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 32 xxh

Find f(x) and g(x).

Think ; I have the square root of“something” . The “something” is g(x), under a square root

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

xgfxgfxh

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 32 xxh

Find f(x) and g(x).

Think ; I have the square root of“something” . The “something” is g(x), under a square root

xxf

xxg

)(

32)(

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.

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 : xgfxxgx

xf ofdomain thefind ,3)( and 1

)( If

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 : xgfxxgx

xf ofdomain thefind ,3)( and 1

)( If

The domian of ƒ(x) is all real numbers except zero…

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

EXAMPLE : xgfxxgx

xf ofdomain thefind ,3)( and 1

)( If

3

1

3

xxgf

xfxgfxgf

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 …

COMBINING FUNCTIONS

COMPOSITE FUNCTIONS :

EXAMPLE : xgfxxgx

xf ofdomain thefind ,3)( and 1

)( If

3

03

3

1

3

x

x

xxgf

xfxgfxgf

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.