**Composite Functions**

Starter

f(x) = 3x + 4 g(x) = x - 5

(a) Find f(5)

(b) Find g(your answer to (a))

(c) Find g(5)

(d) Find f(your answer to (c)).

Comment on your the answers to (b) and (d)

Main Activity

Complete the composite function worksheet

Composite functions

A composite function is a function built out of two or more functions.

The function fg(x) is a composite that means "first do g to x, then do f to the result".

**L.O. - Understand how to form the**

composite of 2 functions (Grade 6+)

composite of 2 functions (Grade 6+)

Starter

f(x) = 3x + 4 g(x) = x - 5

(a) Find f(5)

= 19

(b) Find g(your answer to (a)):

g(19) = 356

(c) Find g(5)

= 20

(d) Find f(your answer to (c)):

f(20) = 64

It makes a big difference which order you use the

functions.

Writing Composites

f(x) = 3x + 4 g(x) = x - 5

(a) Find the composite fg(x)

(b) Find the composite gf(x)

(c) Find the composite ff(x)

2

2

2

Writing Composites

f(x) = 3x + 4 g(x) = x - 5

(a) Find the composite fg(x)

(b) Find the composite gf(x)

(c) Find the composite ff(x)

2

x

-5

2

x - 5

2

x 3 + 4

3(x - 5) + 4 = 3x - 11

2

2

x

x 3 + 4

3x + 4

2

-5

(3x + 4) - 5 =

9x + 24x + 11

2

2

x

x 3 + 4

3x + 4

x 3 + 4

3(3x + 4) + 4 = 9x + 16

Dice of Ultimate Power

1) Give a key word for the lesson.

2) Summarise one key point for the

lesson.

3) Explain one thing you have learned this

lesson.

4) State one thing you still don't understand following this lesson.

5) Suggest one thing you would like to find out

based on this lesson.

6) Free choice from 1 to 5, or another you make

up.

Main Activity

(a) -3 (b) -4 (c) 17 (d) 86 (e) 5 (f) -7 (g) 41 (h) 26

(a) 2(1 - 3x) + 1 = 3 - 6x

(b) 2(2x + 1) + 1 = 4x + 3

(c) 2(x + 4) + 1 = 2x + 9

(d) (2x + 1) + 4 = 4x + 4x + 5

(e) 1 - 3(x + 4) = -3x - 11

(f) 1 - 3(1 - 3x) = 9x - 2

(g) (1 - 3x) + 4 = 9x - 6x + 5

(h) 1 - 3(2x + 1) = -6x - 2

2

2

2

2

2

2

2

2

(a) 3 + 2(4 - x) = 11 - 2x

(b) 2(3 + 2x) + 7 = 8x + 24x + 25

(c) 4 - (2x + 7) = -2x - 3

(d) 3 + 2(3 + 2x) = 9 + 4x

(e) 3 + 2(2x + 7) = 4x + 17

(f) 4 - (4 - x) = x

(g) 4 - (3 + 2x) = 1 - 2x

(h) 2(4 - x) + 7= 2x - 16x + 39

2

2

2

2

2

2

2

2

(a) fg(x)

(b) gf(x)

(c) gg(x)

(d) ff(x)

(e) gff(x)

(f) gfg(x)

**Key**

Examples

Examples

**Activities**

**Activity**

Answers

Answers

**Worked**

Example

Example

Extra example for 10b2

f(x) = 7 - 3x g(x) =

3

x

Find gf(x)

Find fg(x)

Find ff(x)

Find gg(x)

Extra example for 10b2

f(x) = 7 - 3x g(x) =

3

x

Find gf(x)

Find fg(x)

Find ff(x)

Find gg(x)

x-3

+ 7

reciprocal

x3

gf(x) = 3

7-3x

x-3

+ 7

reciprocal

x3

fg(x) = + 7

-9

x

x-3

+ 7

x-3

+ 7

ff(x) = -3(7 - 3x) + 7 = 9x -14

reciprocal

x3

reciprocal

x3

gg(x) = x

**Worked**

Example

Example

Extra starter for 10b2

f(x) = 7 - 3x g(x) =

3

x

Find f(2)

Find g(2)

Find fg(2)

Find gf(2)

Extra starter for 10b2

f(x) = 7 - 3x g(x) =

3

x

Find f(2)

= 1

Find g(2)

=

1

Find fg(2)

= -2

Find gf(2)

= 3

1

2

1

2