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# Composite Functions

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## Mr Mattock

on 13 November 2015

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#### Transcript of Composite Functions

Composite Functions
Starter
f(x) = 3x + 4 g(x) = x - 5

(a) Find f(5)

(c) Find g(5)

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+)

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

(a) Find f(5)
= 19

g(19) = 356

(c) Find g(5)
= 20

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

Activities
Activity

Worked
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

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
Full transcript