O O

O O

(4)(4)

O O

O O

(5)(5)

(6)(6)

O O

(2)(2)

(3)(3)

O O

(1)(1)

O O

O O

O O

TUGAS 11. Mencari solusi dari (fogogof)(x)

fdx/x3Cx2;

f := x/x3Cx2

gdx/x2K1;

g := x/x2K1

f@ g@ g@f x ;

x3Cx22K1

2

K1

3

C x3Cx22K1

2

K1

2

2. Mencari invers dari fungsi berikut :

restart;

hdx/ 1 / 6Cx C 110 /abs x ;

h := x/1

6CxC

110

x

finv % ;

finv x/1

6CxC

110

x

finvd x/solve h@i x = x, i x ;finv := x/solve h@i x = x, i x

finv x ;

(9)(9)

O O

(11)(11)

O O

O O

(12)(12)

O O

(13)(13)

(10)(10)

O O

O O

(8)(8)

O O

O O

O O

O O

i x =1

2 111K6 xC 12321C1308 xC36 x2

x, i x =

1

2

i x =1

2 111K6 xC 12321C1308 xC36 x2

x, i x =

1

2 K109K6 xC 11881K13

x

i x =1

2 K109K6 xC 11881K1

x

i x =1

2 K109K6 xC 11881K1332 xC36 x2

x, i x =K

i x =K1

2 109C6 xC 11881K1

x

i x = i x

3. Memberikan cara dan hasil yang benar pada x, y dan z dari fungsi dibawah ini :

restart;

fd x, y, z / xCyCz = 3;

f := x, y, z /xCyCz = 3

gd x, y, z /4$ xC7$ yC12$ z = 23;g := x, y, z /4 xC7 yC12 z = 23

hd x, y, z /xC10$ zC4$ y = 15;h := x, y, z /xC10 zC4 y = 15

solve xCyCz = 3, 4$ xC7$ yC12$ z = 23, xC10$ zC4$ y = 15 , x, y, z ;x = 1, y = 1, z = 1

4. a.) Mencari nilai akar dari fungsi berikut :

restart;

fdx/ x4C3$ x3C2$ x2C3$ xC1

f := x/x4C3 x3C2 x2C3 xC1

solve f x ;

I, KI, K3

2C

1

2 5 , K

3

2K

1

2 5

O O

(16)(16)

O O

O O

O O

(18)(18)

O O

O O

O O

O O

(17)(17)

O O

(20)(20)

O O

O O

(22)(22)

O O

O O

(14)(14)

(21)(21)

(19)(19)

4.b) Mencari nilai f(9) dari fungsi berikut :

restart;

fdx/ log sqrt 100$ x C100$ x99Cln x / 55$ xK10

f := x/log 100 x C100 x99Cln x

55 xK10

f 9 ;1

485 ln 30

C330861305504297506960452395472628718545034087665772127769275353886866956040665418

evalf f 9 ;

6.085085656 1093

5. Mencari fungsi polimon yang masing-masing derajadnya berbeda serta mencari nilai akarnya

restart;a.

adx/2$x4C2$x3C2$x2C 2$x

a := x/2 x4C2 x3C2 x2C2 x

factor a x ;

2 x xC1 x2C1

solve a x ;0, K1, I, KI

b.

bdx/3$x5C3$x4C3$x3C3$x2C3$x2C3$x

b := x/3 x5C3 x4C3 x3C6 x2C3 x

factor b x ;

3 x xC1 x3CxC1

solve b x ;

0, K1, K1

6 108C12 93

1 / 3C

2

108C12 931 / 3

,1

12 108

C12 931 / 3

K1

108C12 931 / 3

C1

2 I 3 K

1

6 108

O O

(29)(29)

(23)(23)

O O

O O

O O

(26)(26)

O O

(28)(28)

O O

(30)(30)

(27)(27)

O O

O O

O O

(24)(24)

O O

(25)(25)

O O

O O

(31)(31)

C12 931 / 3

K2

108C12 931 / 3

,1

12 108C12 93

1 / 3

K1

108C12 931 / 3

K1

2 I 3 K

1

6 108C12 93

1 / 3

K2

108C12 931 / 3

c.

cdx/4$x6C4$x5C4$x4C4$x3C4$x2C4$x

c := x/4 x6C4 x5C4 x4C4 x3C4 x2C4 x

factor c x ;

4 x xC1 x2CxC1 x2KxC1

solve c x ;

0, K1, K1

2C

1

2 I 3 , K

1

2K

1

2 I 3 ,

1

2C

1

2 I 3 ,

1

2K

1

2 I 3

d.

ddx/2$x6C2$x5C2$x4C2$x3

d := x/2 x6C2 x5C2 x4C2 x3

factor d x ;

2 x3 xC1 x2C1

solve d x ;0, 0, 0, K1, I, KI

e.

edx/5$x4C3$x2Cx

e := x/5 x4C3 x2Cx

factor e x ;

x 5 x3C3 xC1

solve e x ;

0, K1

10 100C60 5

1 / 3C

2

100C60 51 / 3

,1

20 100C60 5

1 / 3

O O

K1

100C60 51 / 3

C1

2 I 3 K

1

10 100C60 5

1 / 3

K2

100C60 51 / 3

,1

20 100C60 5

1 / 3K

1

100C60 51 / 3

K1

2 I 3 K

1

10 100C60 5

1 / 3K

2

100C60 51 / 3