Kisi Kisi PAT Matematika Kelas XI no 35

35. Diketahui 𝑓(𝑥) = (2𝑥 + 1) / (𝑥 − 2), maka 𝑓 ⁻¹(7) = ...

a. 0,5

b. 1,5

c. 3,0

d. 3,5

e. 4,5

Jawaban :

𝑓(𝑥) = (2𝑥 + 1) / (𝑥 − 2)

f(x) berbentuk : (ax + b) / (cx + d)

untuk mencari fungsi inversnya, terdapat cara cepatnya yaitu :

𝑓 ⁻¹(x) = (- dx + b) / (cx - a)

dalam soal ini, 

a = 2

b = 1

c = 1

d = - 2

𝑓 ⁻¹(x) = (2x + 1) / (x - 2)

𝑓 ⁻¹(7) = (2 . 7 + 1) / (7 - 2)

𝑓 ⁻¹(7) = (14 + 1) / 5

𝑓 ⁻¹(7) = 15 / 5

𝑓 ⁻¹(7) =  3

Jawaban : C

Kisi Kisi PAT Matematika Kelas XI no 34

34. Jika 𝑓(𝑥)=4𝑥^2 − 1, maka 𝑓 ⁻¹(𝑥)=...

a. 1/2 √(𝑥 + 1)

b. 1/2 √(𝑥 − 1)

c. 1/3 √(𝑥 + 1)

d. 1/3 √(𝑥 − 1)

e. 1/4 √(𝑥 − 1)

Jawaban :

𝑓(𝑥)=4𝑥^2 − 1

y = 4x^2 - 1

4x^2 = y + 1

x^2 = 1/4 (y + 1)

x = 1/2 √(y + 1)

𝑓 ⁻¹(y) = 1/2 √(y + 1)

𝑓 ⁻¹(x) = 1/2 √(x + 1)

Jawaban : A

Kisi Kisi PAT Matematika Kelas XI no 33

33. Jika 𝑓(𝑥) = 3𝑥 − 1, maka 𝑓 ⁻¹(𝑥)=...

a. (𝑥 + 1) / 2

b. (𝑥 + 1) / 3

c. 2 / (𝑥 + 1)

d. 3 / (𝑥 + 1)

e. 1/3𝑥 + 1

Jawaban :

𝑓(𝑥) = 3𝑥 − 1

y = 3x - 1

3x = y + 1

x = 1/3 (y + 1)

𝑓 ⁻¹(y) = 1/3 (y + 1)

𝑓 ⁻¹(x) = 1/3 (x + 1)

𝑓 ⁻¹(x) = (x + 1) / 3

Jawaban : B

Kisi Kisi PAT Matematika Kelas XI no 32

32. Jika 𝑔(𝑥) = 4𝑥 + 3 dan (𝑓 𝑜 𝑔)(𝑥) = 8𝑥 − 6, maka rumus 𝑓(𝑥) = ...

A. 2𝑥 − 14

B. 2𝑥 − 12

C. 2𝑥 − 10

D. 2𝑥 − 8

E. 2𝑥 − 6

Jawaban :

𝑔(𝑥) = 4𝑥 + 3

(𝑓 𝑜 𝑔)(𝑥) = 8𝑥 − 6

f (g (x)) = 8x - 6

f (4x + 3) = 8x - 6

misalkan :

a = 4x + 3

4x = a - 3

x = 1/4 (a - 3)

f (4x + 3) = 8x - 6

f (a) = 8 (1/4 (a - 3)) - 6

f (a) = 2 (a - 3) - 6

f (a) = 2a - 6 - 6

f (a) = 2a - 12

sehingga,

f (x) = 2x - 12

Jawaban : B

Kisi Kisi PAT Matematika Kelas XI no 31

31. Diketahui 𝑔(𝑥) = 3𝑥 + 2 dan (𝑓 𝑜 𝑔)(𝑥) = 6𝑥 − 4, maka rumus 𝑓(𝑥)= ...

A. 2𝑥 − 14

B. 2𝑥 − 12

C. 2𝑥 − 10

D. 2𝑥 − 8

E. 2𝑥 − 6

Jawaban :

𝑔(𝑥) = 3𝑥 + 2 

(𝑓 𝑜 𝑔)(𝑥) = 6𝑥 − 4

f (g (x)) = 6x - 4

f (3x + 2) = 6x - 4

misalkan :

a = 3x + 2

3x = a - 2

x = 1/3 (a - 2)

f (3x + 2) = 6x - 4

f (a) = 6 (1/3 (a - 2)) - 4

f (a) = 2(a - 2) - 4

f (a) = 2a - 4 - 4

f (a) = 2a - 8

maka, 

f (x) = 2x - 8

Jawaban : D

Kisi Kisi PAT Matematika Kelas XI no 30

30. Jika 𝑓(𝑥) = 2𝑥 − 3 dan (𝑓 𝑜 𝑔)(𝑥) = 8𝑥 − 7 maka 𝑔(𝑥)=...

A. 4𝑥 − 3

B. 4𝑥 − 2

C. 4𝑥 − 1

D. 4𝑥 + 1

E. 4𝑥 + 2

Jawaban :

𝑓(𝑥) = 2𝑥 − 3

(𝑓 𝑜 𝑔)(𝑥) = 8𝑥 − 7

f (g (x)) = 8x - 7

2(g (x)) − 3 = 8x - 7

2 g(x) = 8x - 7 + 3

2 g(x) = 8x - 4

g(x) = 4x - 2

Jawaban : B

Kisi Kisi PAT Matematika Kelas XI no 29

29. Diketahui 𝑓(𝑥) = 𝑥^2 + 5 dan (𝑓 𝑜 𝑔)(𝑥) = 𝑥^2 − 2𝑥 + 6. Rumus 𝑔(𝑥) = ...

A. 2𝑥 + 2

B. 2𝑥 + 1

C. 𝑥 + 1

D. 2𝑥 − 1

E. 𝑥 − 1

Jawaban :

𝑓(𝑥) = 𝑥^2 + 5

(𝑓 𝑜 𝑔)(𝑥) = 𝑥^2 − 2𝑥 + 6

f (g(x)) = 𝑥^2 − 2𝑥 + 6

g(x)^2 + 5 = 𝑥^2 − 2𝑥 + 6

g(x)^2 = 𝑥^2 − 2𝑥 + 6 - 5

g(x)^2 = 𝑥^2 − 2𝑥 + 1

g(x)^2 = (x - 1)(x - 1)

g(x)^2 = (x - 1)^2

g(x) = x - 1

Jawaban : E

Kisi Kisi PAT Matematika Kelas XI no 28

28. Jika 𝑓(𝑥) = 𝑥^2 + 2𝑥 dan 𝑔(𝑥) = 𝑥 − 1, nilai (𝑓 𝑜 𝑔)(8)= ...

a. 63

b. 62

c. 61

d. 60

e. 59

Jawaban :

𝑓(𝑥) = 𝑥^2 + 2𝑥

𝑔(𝑥) = 𝑥 − 1

(𝑓 𝑜 𝑔)(8) = f (g (8))

(𝑓 𝑜 𝑔)(8) = f (8 - 1)

(𝑓 𝑜 𝑔)(8) = f (7)

(𝑓 𝑜 𝑔)(8) = 7^2 + 2 (7)

(𝑓 𝑜 𝑔)(8) = 49 + 14

(𝑓 𝑜 𝑔)(8) = 63

Jawaban : A

Kisi Kisi PAT Matematika Kelas XI no 27

27. Diberikan 𝑓(𝑥) = 𝑥^2 + 2 dan 𝑔(𝑥) = 𝑥^2 − 2. Hasil dari (𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥)= ...

a. 8𝑥^2 + 4

b. 8𝑥^2 − 4

c. −8𝑥^2 + 4

d. 4

e. −4

Jawaban :

𝑓(𝑥) = 𝑥^2 + 2

𝑔(𝑥) = 𝑥^2 − 2

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = g (f (x)) - f (g(x))

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = g (𝑥^2 + 2) - f (𝑥^2 − 2)

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = (𝑥^2 + 2)^2 − 2 - ((𝑥^2 − 2)^2 + 2)

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = (𝑥^4 + 4x^2 + 4)− 2 - ((𝑥^4 − 4x^2 + 4) + 2)

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = 𝑥^4 + 4x^2 + 4 − 2 - 𝑥^4 + 4x^2 - 4 - 2

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = 𝑥^4 + 4x^2 + 2 - 𝑥^4 + 4x^2 - 6

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = 8x^2 - 4

Jawaban : B

Kisi Kisi PAT Matematika Kelas XI no 26

26. Jika 𝑓(𝑥) = 3 / (4𝑥 − 2) dan 𝑔(𝑥) = 3 − 5𝑥, maka (𝑓 𝑜 𝑔)(𝑥)= ...

a. (12𝑥 − 21) / (4𝑥 + 2)

b. (12𝑥 − 21) / (4𝑥 − 2)

c. (12𝑥 + 21) / (4𝑥 + 2)

d. 3 / (10 + 20𝑥)

e. 3 / (10 − 20𝑥)

Jawaban :

𝑓(𝑥) = 3 / (4𝑥 − 2)

𝑔(𝑥) = 3 − 5𝑥

(𝑓 𝑜 𝑔)(𝑥) = f (g (x))

(𝑓 𝑜 𝑔)(𝑥) = f (3 - 5x)

(𝑓 𝑜 𝑔)(𝑥) = 3 / (4 (3 - 5x) - 2)

(𝑓 𝑜 𝑔)(𝑥) = 3 / (12 - 20x - 2)

(𝑓 𝑜 𝑔)(𝑥) = 3 / (10 - 20x)

Jawaban : E

Kisi Kisi PAT Matematika Kelas XI no 25

25. Jika 𝑓(𝑥) = 3𝑥 + 1 dan 𝑔(𝑥) = 2𝑥 − 3, maka (𝑔 𝑜 𝑓)(𝑥)=...

A. 6𝑥 − 1

B. 6𝑥 + 1

C. 6𝑥 − 8

D. 8𝑥 − 6

E. 8𝑥 + 6

Jawaban :

𝑓(𝑥) = 3𝑥 + 1

𝑔(𝑥) = 2𝑥 − 3

(𝑔 𝑜 𝑓)(𝑥) = g (f (x))

(𝑔 𝑜 𝑓)(𝑥) = g (3x + 1)

(𝑔 𝑜 𝑓)(𝑥) = 2(3x + 1) - 3

(𝑔 𝑜 𝑓)(𝑥) = 6x + 2 - 3

(𝑔 𝑜 𝑓)(𝑥) = 6x - 1

Jawaban : A

Kisi Kisi PAT Matematika Kelas XI no 24

24. Jika 𝑓(𝑥) = 3𝑥 + 2 dan 𝑔(𝑥) = 2 − 𝑥, maka (𝑔 𝑜 𝑓)(𝑥)= ...

a. −3𝑥

b. 3𝑥

c. − 3𝑥 − 4

d. −3𝑥 + 2

e. 3x - 2

Jawaban :

 𝑓(𝑥) = 3𝑥 + 2

𝑔(𝑥) = 2 − 𝑥

(𝑔 𝑜 𝑓)(𝑥) = g (f (x))

(𝑔 𝑜 𝑓)(𝑥) = g (3x + 2)

(𝑔 𝑜 𝑓)(𝑥) = 2 - (3x + 2)

(𝑔 𝑜 𝑓)(𝑥) = 2 - 3x - 2

(𝑔 𝑜 𝑓)(𝑥) = - 3x

Jawaban : A

Kisi Kisi PAT Matematika Kelas XI no 23

23. Jika 𝑓(𝑥) = 3𝑥 + 2 dan 𝑔(𝑥) = 2 − 𝑥, maka (𝑓 𝑜 𝑔)(𝑥)= ...

A. 3𝑥 + 8

B. 3𝑥 − 8

C. −3𝑥 + 8

D. 3𝑥 + 2

E. 3𝑥 − 2

Jawaban :

𝑓(𝑥) = 3𝑥 + 2

𝑔(𝑥) = 2 − 𝑥

(𝑓 𝑜 𝑔)(𝑥) = f (g (x) )

(𝑓 𝑜 𝑔)(𝑥) = f (2 - x)

(𝑓 𝑜 𝑔)(𝑥) = 3 (2 - x) + 2

(𝑓 𝑜 𝑔)(𝑥) = 6 - 3x + 2

(𝑓 𝑜 𝑔)(𝑥) = 8 - 3x

(𝑓 𝑜 𝑔)(𝑥) = - 3x + 8

Jawaban : C

Kisi Kisi PAT Matematika Kelas XI no 22

22. Diketahui 𝑓(𝑥) = 2𝑥 + 1 dan 𝑔(𝑥) = 2 − 4𝑥, tentukanlah nilai dari (𝑔 / 𝑓)(3)!

a. 1 3/7

b. 3/7

c. −3/7

d. −1 3/7

e. 1 7/3

Jawaban :

𝑓(𝑥) = 2𝑥 + 1

𝑔(𝑥) = 2 − 4𝑥

(𝑔 / 𝑓)(3) = g(3) / f(3)

kita hitung g(3) dan f(3) terlebih dahulu ya ~

𝑔(𝑥) = 2 − 4𝑥

g(3) = 2 - 4 (3)

g(3) = 2 - 12

g(3) = - 10

𝑓(𝑥) = 2𝑥 + 1

f(3) = 2(3) + 1

f(3) = 6 + 1

f(3) = 7

(𝑔 / 𝑓)(3) = g(3) / f(3)

(𝑔 / 𝑓)(3) = - 10 / 7

(𝑔 / 𝑓)(3) = - 1 3/7

Jawaban : D

Kisi Kisi PAT Matematika Kelas XI no 21

21. Jika 𝑓(𝑥) = (6𝑥 − 2) / (1 − 3𝑥) dan 𝑔(𝑥)=√(9 − 2𝑥), nilai dari (𝑓 . 𝑔)(3) adalah ...

a. −2√3

b. −√3

c. √3

d. 2√3

e. 3√3

Jawaban :

𝑓(𝑥) = (6𝑥 − 2) / (1 − 3𝑥)

𝑔(𝑥)=√(9 − 2𝑥)

(𝑓 . 𝑔)(3) = f(3) . g(3) 

kita hitung f(3) dan g(3) terlebih dahulu ya ~

𝑓(𝑥) = (6𝑥 − 2) / (1 − 3𝑥)

f (3) = (6 . 3 - 2) / (1 - 3 . 3)

f (3) = (18 - 2) / (1 - 9)

f (3) = 16 / (-8)

f (3) = - 2

𝑔(𝑥)=√(9 − 2𝑥)

g (3) = √(9 − 2 . 3)

g (3) = √(9 − 6)

g (3) = √3

(𝑓 . 𝑔)(3) = f(3) . g(3) 

(𝑓 . 𝑔)(3) = (- 2) . √3

(𝑓 . 𝑔)(3) = - 2√3

Jawaban : A