1 Functions - Form4 Add Math

SULIT 5 3472/1

3472/1 [ Lihat halaman sebelah SULIT

2

The functions f –1 and fg are defined as f –1 : x → 4 − 3x and fg : x → x − 3. Find Fungsi-fungsi f –1 dan fg ditakrifkan sebagai f –1: x → 4 − 3x dan fg : x → x − 3. Cari (a) f −1(3). (b) g(x)

[3 marks] [3 markah]

Answer/Jawapan:

(a) (b)

3 Given that function 2 3f x x and g x k x . Find the value of

Diberi fungsi 2 3f x x dan g x k x . Cari nilai bagi (a) 2f ,

(b) k if 1 11fg .

k jika 1 11fg .

[3 marks] [3 markah]

Answer/Jawapan:

(a) (b)

3

3

3

2

For examiner’s

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SULIT 4 3472/1

3472/1 SULIT

Answer all questions. Jawab semua soalan.

1

Diagram 1 shows the relation between x and f(x). Rajah 1 menunjukkan hubungan antara x dan f(x).

Diagram 1 Rajah 1 State Nyatakan (a) the object of 9 , objek bagi 9 , (b) the type of relation between x and f(x). jenis hubungan antara x dan f(x).

[2 marks] [2 markah]

Answer/Jawapan:

(a) (b)

For examiner’s

use only

2

1

9

6

3

0 1 2 − 1

f(x)

x ●

●

●

●

− 2

●

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SULIT 5 3472/1

3472/1 [ Lihat halaman sebelah SULIT

2

The functions f –1 and fg are defined as f –1 : x → 4 − 3x and fg : x → x − 3. Find Fungsi-fungsi f –1 dan fg ditakrifkan sebagai f –1: x → 4 − 3x dan fg : x → x − 3. Cari (a) f −1(3). (b) g(x)

[3 marks] [3 markah]

Answer/Jawapan:

(a) (b)

3 Given that function 2 3f x x and g x k x . Find the value of

Diberi fungsi 2 3f x x dan g x k x . Cari nilai bagi (a) 2f ,

(b) k if 1 11fg .

k jika 1 11fg .

[3 marks] [3 markah]

Answer/Jawapan:

(a) (b)

3

3

3

2

For examiner’s

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11

3472/1

(Answer all questions) Jawab semua soalan

1. Diagram 1 shows the graph of function ( ) 2 4f x x for domain 0 5x

Rajah 1 menunjukkan graf bagi fungsi ( ) 2 4f x x , untuk domain 0 5x .

Diagram 1 / Rajah 1

State Nyatakan

(a) f (0), (b) range of f(x) corresponding to the given domain.

julat f(x) berdasarkan domain yang diberi. [2 markah] Answer / Jawapan :

(a) (b)

2. Given the function ( ) 3 2g x x and ( ) 12 4gh x x , Diberi fungsi ( ) 3 2g x x dan ( ) 12 4gh x x ,

find / cari

(a) h(x), (b) value of x such that h(x) maps onto itself.

nilai x dengan keadaan h(x) memeta kepada dirinya sendiri. Answer / Jawapan:

(a) (b)

[3 markah]

y

x O

4 ●

● (5, 6)

● 2

y = f(x)

2

1

3

2

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22

3472/1

3. Diagram 3 shows the function 5: kxxf , where k is a constant. Rajah 3 menunjukkan fungsi 5: kxxf , dengan keadaan k ialah pemalar.

Diagram 3 / Rajah 3 Find the value of k Cari nilai k. [3 markah]

Answer / Jawapan :

4. Straight line 1x2y is tangent to the curve 2 .y x p

Garis lurus 1x2y ialah tangen kepada lengkung 2 .y x p

Find the value of p Cari nilai p.

[3 markah] Answer / Jawapan :

3

14

kx+5 f

x

3

4

3

3

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Answer all questions.Jawab semua soalan

1 Diagram 1 shows the linear function f.Rajah 1 menunjukkan fungsi linear f.

Diagram 1Rajah 1

State:Nyatakan:

(a) value of mnilai m

(b) value of nnilai n

(c) image of 10imej bagi 10

[3 marks][3 markah]

Answer / Jawapan :

(a)

(b)

(c)

Forexaminer’s

use only

3

1

1 2

m 4

3 n

4 8

x f(x)

4

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2 Given function g and h as g(x) = 2x – 3 and h(x) = 2x2 + 2. Find hg(x).Fungsi g dan h diberi sebagai g(x) = 2x – 3 dan h(x) = 2x2 + 2. Cari hg(x).

[3 marks][3 markah]

Answer / Jawapan :

3 Find f – 1 (x) given f(x) = –2 x +10.Cari f – 1 (x) diberi f(x) = –2 x +10.

[2 marks][2 markah]

Answer/ Jawapan :

Forexaminer’s

use only

3

2

2

3

5

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SULIT 7 3472/1

Answer all questions. Jawab semua soalan.

1 The following information shows set A, set B and the relation between set A and set B

in the form of ordered pairs.

Maklumat berikut menunjukkan set A, set B dan hubungan antara set A dan set B dalam bentuk pasangan tertib.

A = {p, k, w}

B = {2, 3, 4, 5, 6}

{( p, 2 ),( p, 3 ),( k, 3 ),( w, x )}

Given that the range of the relation between set A and set B is { 2, 3, 4 }, state

Diberi julat hubungan antara set A dan set B ialah { 2, 3, 4 }, nyatakan

(a) the image of k,

imej bagi k,

(b) the value of x.

nilai x.

(c) the type of the relation.

jenis hubungan itu. [3 marks]

[3 markah]

Answer / Jawapan :

(a)

(b)

(c)

[Lihat sebelah]

For Examiner’s

Use

1

3

Negeri Sembilan SPM 2013 http://edu.joshuatly.com/

SULIT 8 3472/1

2 Given that xxh 5)( and 3)( kxxg , find

Diberi bahawa xxh 5)( dan 3)( kxxg , cari

(a) )1(h ,

(b) the value of k such that 7)1( gh .

nilai k dengan keadaan 7)1( gh [3 marks] [3 markah]

Answer / Jawapan :

(a)

(b)

3 Given that 56: xxf and 2

3:

xxg, find the function 1fg .

Diberi bahawa 56: xxf dan 2

3:

xxg, cari fungsi 1fg .

[3 marks]

[ 3 markah]

Answer / Jawapan :

For Examiner’s

Use

2

3

3

3

[Lihat sebelah] Negeri Sembilan SPM 2013 http://edu.joshuatly.com/

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5

SULIT 3472/1

3472/1 ©2013 Hak Cipta BPSBPSK SULIT

Answer all questions.

Jawab semua soalan.

1. Diagram 1 shows the linear function f.

Rajah 1 menunjukkan fungsi linear f.

(a) State the value of k.

Nyatakan nilai k.

(b) Using the function notation, express f in terms of x.

Menggunakan tata tanda fungsi, ungkapkan f dalam sebutan x.

[ 2 marks ]

[2 markah]

Answer/Jawapan :

(a)

(b)

2. Given the function : 7 2g x x , find the value of n such that 1(3 1)g n n .

Diberi fungsi : 7 2g x x , cari nilai n dengan keadaan 1(3 1)g n n .

[ 3 marks ]

[3 markah]

Answer/Jawapan :

Diagram 1

Rajah 1

x f(x)

-1

4

1

2

-2

8

k

2

3

2

2

1

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6

SULIT 3472/1

3472/1 ©2013 Hak Cipta BPSBPSK SULIT

3. Given the function ( ) 3h x px and 2 ( ) 49h x x q , where p and q are constants

and 0.p

Find the value of p and of q.

Diberi fungsi ( ) 3h x px dan 2 ( ) 49h x x q , dengan keadaan p dan q adalah

pemalar dan 0.p

Cari nilai p dan nilai q.

[ 3 marks ]

[3 markah]

Answer/Jawapan :

4. It is given that m and 2 are the roots of the quadratic equation

25 ( 1) 2 0x n x .

Find the value of m and of n.

Diberi bahawa m dan 2 adalah punca-punca bagi persamaan kuadratik

25 ( 1) 2 0x n x .

Cari nilai m dan nilai n.

[ 3 marks ]

[3 markah]

Answer/Jawapan :

3

3

For

Examiner’s Use

3

4

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