sinar functions

7/29/2019 SINAR Functions

1/5

FUNCTIONS

1 Given functionf:x 2x 6, find the

Diberi fungsi f : x 2x 6, cari

(a) image of 7

imej 7(b) object which has the image 16

objek yang mempunyai imej 16

2 Diagram 1 represents a functionf:x x2 + bx + c.

Rajah 1 mewakili fungsi f: x x2 + bx + c.

Diagram 1

Rajah 1

Find the

Cari

(a) values ofb and c,

nilai b dan c,

(b) the image of 7 under the function.

imej 7 di bawah fungsi itu.

3 Given functionf:x 5x 4, find the

Diberi fungsi f : x 5x 4, cari

(a) image of 3

imej 3

(b) object which has the image 41

objek yang mempunyai imej 41

4 The functions offandgare defined asf:x x + 1 andg:x ,x k. Find

Fungsi-fungsi f dan g ditakrifkan sebagai f : x x + 1 dan g : x , x k. Cari

(a) the value ofk

nilai k(b) the composite functionf2

fungsi gubahan f2

(c) the composite functiongf

fungsi gubahan gf

5 The functions offandgare defined asf:x x + 6 andfg:x x + 9. Find the functiong.

Fungsi-fungsi f dan g ditakrifkan sebagai f : x x + 6 dan fg : x x + 9. Cari fungsi g.

6 The functions offandgare defined asf:x x 2 andg:x . Find the composite function offg

and the value offg(7).

Fungsi-fungsi f dan g ditakrifkan sebagai f : x x 2 dan g : x . Cari fungsi gubahan fg dan

nilai fg(7).


2/5

7 Given the functionf:x ax + b and the composite functionf2 :x 25x + 6, where a and b are

constants and a > 0, find the values ofa and b.

Diberi fungsi f : x ax + b dan fungsi gubahan f2 : x 25x + 6, di mana a dan b ialah pemalar dan

a > 0, cari nilai a dan b.

8 The functions offandgare defined asf:x 7x + 4 andg:x x2 + 8. Find the composite function

ofgfandfg.

Fungsi-fungsi f dan g ditakrifkan sebagai f : x 7x + 4 dan g : x x2 + 8. Cari fungsi gubahan gf

dan fg.

9 Given the functionf:x ax + b and the composite functionf2 :x 36x + 49, where a and b are

constants and a > 0, find the values ofa and b.

Diberi fungsi f : x ax + b dan fungsi gubahan f2 : x 36x + 49, di mana a dan b ialah pemalar dan

a > 0, cari nilai a dan b.

10 The functionfis defined asf:x x + 7. Find

Fungsi f ditakrifkan sebagai f : x x + 7. Cari(a) f1(4)

(b) f1(x)

11 The functionsfandgare defined asf:x x 5 andg:x 5x 2.

Findgf1(x).

Fungsi-fungsi f dan g ditakrifkan sebagai f : x x 5 dan g : x 5x 2.

Cari gf1(x).

12 The functionfis defined asf:x x 5. Find

Fungsi f ditakrifkan sebagai f : x x 5. Cari

(a) f1

(2)(b) f1(x)

13 The functionsfandgare defined asf:x 2x 2 andg:x 5x + 3.

Findgf1(x).

Fungsi-fungsi f dan g ditakrifkan sebagai f : x 2x 2 dan g : x 5x + 3.

Cari gf1(x).

14 The functionsfandgare defined asf:x 6x 2 andg:x 5x + 2.

Findgf1(x).

Fungsi-fungsi f dan g ditakrifkan sebagai f : x 6x 2 dan g : x 5x + 2.

Cari gf

1

(x).

15 The functionfis defined asf:x 7x + 2. Find

Fungsi f ditakrifkan sebagai f : x 7x + 2. Cari

(a) f1(4)

(b) f1(x)

Answer:

1 (a) f(7) = 2(7) 6

= 20

(b) f(x) = 16

2x 6 = 16


3/5

2x = 10

x = 5

2 (a) f(x) =x2 + bx + c

f(5) = 2

(5)2

+ b(5) + c = 225 5b + c = 2

5b + c = 23 E1

f(2) = 16

(2)2 + b(5) + c = 16

4 + 2b + c = 16

2b + c = 12 E2

E1 E2:

7b = 35

b = 5

Substitute b = 5 into E1.

5(5) + c = 23

c = 2

(b) f(x) =x2 + 5x + 2

f(7) = (7)2 + 5(7) + 2

= 49 35 + 2

= 16

3 (a) f(3) = 5(3) 4

= 11

(b) f(x) = 415x 4 = 41

5x = 45

x = 9

4 (a) x + 1 = 0

x = 1

k= 1

(b) f2 =f(f(x))

=f(x + 1)

= (x + 1) + 1

=x + 2

(c) gf(x) =g(f(x))

=g(x + 1)

=

= ,x 2

5 Givenf(x) =x + 6 andfg(x) =x + 9.

Diberi f(x) = x + 6 dan fg(x) = x + 9.

fg(x) =f(g(x))

=g(x) + 6

g(x) + 6 =x + 9

g(x) =x + 3

g:x x + 3


4/5

6 Givenf(x) = x 2 andg(x) = .

Diberi f(x) = x 2 dan g(x) = .

fg(x) =f(g(x))

=f

= 2

=x

2

fg(7) = (7) 2

= 1

7 f2(x) = a(ax + b) + b

= a2b + ab + b

a2 = 25

a = 5

ab+ b = 6

6b = 6

b = 1

8 Givenf(x) = 7x + 4 andg(x) = x2 + 8.Diberi f(x) = 7x + 4 dan g(x) = x2 + 8.

gf(x) =g(f(x))

=g(7x + 4)

= (7x + 4)2 + 8

= (49x2 56x + 16) + 8

= 49x2 + 56x 8

fg(x) =f(g(x))

=f(x2 + 8)

= 7(x2 + 8) + 4

= 7x2 52

9 f2(x) = a(ax + b) + b

= a2b + ab + b

a2 = 36

a = 6

ab+ b = 49

7b = 49

b = 7

10 (a) Letf1(4) = k

Sof(k) = 4

k+ 7 = 4

k= 3Therefore,f1(4) = 3

(b) Letf1(x) =y

Sof(y) =x

y + 7 =x

y =x 7

Therefore,f1(x) =x 7

11 Letf1(x) =y

Sof(y) =x

y 5 =x

y =x + 5

Thereforef1(x) =x + 5

gf1(x) =g(f1(x))


5/5

=g(x + 5)

= 5(x + 5) 2

= 5x + 23

12 (a) Letf1(2) = k

Sof(k) = 2k 5 = 2

k= 7

Therefore,f1(2) = 7

(b) Letf1(x) =y

Sof(y) =x

y 5 =x

y = x 5

Therefore,f1(x) = x 5

13 Letf1(x) =y

Sof(y) =x

2y 2 =xy =

Thereforef1(x) =

gf1(x) =g(f1(x))

=g()

= 5() + 3

=

14 Letf1(x) =y

Sof(y) =x

6y 2 =x

y =Thereforef1(x) =

gf1(x) =g(f1(x))

=g()

= 5() + 2

=

15 (a) Letf1(4) = k

Sof(k) = 4

7k+ 2 = 4

k=

Therefore,f1(4) =

(b) Letf1(x) =ySof(y) =x

7y + 2 =x

7y =x 2

y =

Therefore,f1(x) =

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