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g f f -1 g -1 gf ADDITIONAL MATHEMATICS CHAPTER 1 : FUNCTION BY : cg.aiman FUNCTIONS 1. Arrow diagram 1. Ordered pairs {(2,4),(3,9), (4,16)} 2. Graphs Relations ONE to ONE ONE to MANY MANY to ONE MANY to MANY Function Notation f:x y Or ___________ Function x y z Composite function fg(x) = f [g(x)] inverse function f(x) = y f -1 (y) = x

addmath form 4 Chapter 1 - Function

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ADDITIONAL MATHEMATICSCHAPTER 1 : FUNCTION

BY : cg.aiman

FUNCTIONS

RelationsFunction

inverse functionComposite functionFunction Notation ONE to ONE ONE to MANY MANY to ONE MANY to MANY1. Arrow diagram

1. Ordered pairs{(2,4),(3,9),(4,16)}2. Graphs

f(x) = yf-1(y) = x

fg(x) = f [g(x)]

f:x yOr____________

gffgyzx

f-1g-1

1.0 RelationExpress the relation between the following pairs of set in the form of arrow diagram, ordered pair and graph.Arrow diagramOrdered pairGraph

a) Set A = {Kelantan, Selangor, Johor}

Set B = { Shah Alam, Johor Bharu, Kota Bharu}Relation: City of the state in Malaysia

b) Set A = {Triangle, rectangle, pentagon}

Set B = { 3, 4, 5 }Relation: Number of edge

c) Set A = { 9, 16, 4}

Set B = { 4, 2 3}Relation: Square root of number

d) Set x = { 2, 5, 6, 7}

Set y = { 4, 12, 10, 14}Relation: 2x

1.1 Determine domain, codomain, object, image and range of relationList down the domain, codomain, object, image and range of the following realtion

Domain = {}Codomain = {.}Object = Image = ..Range = {}

1.2 Classifying the types of the relations

State the type of the following relation

2.0 Function

a) Find the image for each of the following functioni)f:x 2x + 9 f(5) =

ii)g:x + 6 find g(-3)

iii)h(x) = x - 3 find h(4) and h(-3).

b) Find the object for each of the following functioni) f(x) = 2x + 7 for which f(x) =3

ii) g(x) = for which g(x) = 4iii) h(x) = x - 3 for which have the image 5.

EXERCISE (CLONE PASS YEAR SPM)1. Given the function f:x x - 2, find the values of x such that f(x) = 6.2007 paper 1:question 2

2. It is given that the function f(x)= p 3x, where p is a constant. Find the value of p such that f (p) = 42012 paper 1: question 3

3.0 Composite function3.1 a) Find the following composite functions.i)f(x) = 2x + 3 g(x) = 1-x fg(x) =

ii) g(x) = 2 +5x find g2(x)iii) g(x) = 1 - h(x) = gh(x)=

3.1 b) Find the value for each of the following composite functions.i)f(x) = 2x + 3 g(x) = 1-x fg(4) ii) f(x) = 2x + 3 g(x) = 2 + 5x2 gf(3) = iii) f(x) = 2x + 1 g(x) = ax2 + b gf(x) = 12x2 + 12x + 7 a)find a and b b) find g2(5)

3.1 c) Solve

EXERCISE (CLONE PASS YEAR SPM)1. Given the function h(x) = , x 0 and the composite function hg(x) = 4x, find a) g(x)b) the value of x when gh(x) = 82004 Paper 1: question 3

2. k : x px + q, where p and q are constants, and p > 0.k2 : x 25x + 42

Find the values of p and q.2007: paper 1:question3

4.0 Inverse functionf(x) = yf-1(y) = x

a) Find the inverse function of each of the following functions.

b) Find the inverse function of each of the following function in term of p and q.

Solving composite and inverse functiona) Given that f (x) = ax +b and f-1 (x) = , findi)The values of a and bii) The value of f(-6)iii)The value of ff-1(3)

b) Given the functions g (x) = 3x +1 and h(x) = x2 x + 2, findi)the value of g-1(2)ii)the composite function hg(x).

SPM PASS Year Exam

1. (spm 2014,paper 1, Q1)

2. (Spm 2014, paper 1,Q2)

3. (spm 2014, paper 2, Q3)

4. (spm 2013, paper 1, Q1)

5. (spm 2013, paper 1, Q2)

6. (spm 2013, paper 1, Q3)

7. (spm, 2012, paper 1, Q1)

8. (spm 2012, paper 1, Q2)

9. (spm 2012, paper 1, Q3)