Fungsi Komposisi & Fungsi Invers

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| By Ardianto81

Ardianto81

Community Contributor

Quizzes Created: 1 | Total Attempts: 1,448

Questions: 20 | Attempts: 1,455 | Updated: Mar 22, 2023

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Fungsi Komposisi & Fungsi Invers - Quiz

Questions and Answers

1.

Jika f(x) = 3x + 4, maka nilai dari f(5) adalah ...
- A.
  
  7
- B.
  
  10
- C.
  
  13
- D.
  
  16
- E.
  
  19
Correct Answer
E. 19

Explanation
The given function f(x) = 3x + 4 represents a linear equation in the form y = mx + c, where m is the slope and c is the y-intercept. In this case, the slope is 3 and the y-intercept is 4. To find the value of f(5), we substitute x = 5 into the equation. Thus, f(5) = 3(5) + 4 = 15 + 4 = 19. Therefore, the correct answer is 19.

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2.

Jika maka nilai dari f(3) adalah ...
- A.
  
  40
- B.
  
  41
- C.
  
  38
- D.
  
  39
- E.
  
  37
Correct Answer
B. 41
3.

Jika fungsi dan didefinisikan dengan dan , maka
- A.
- B.
- C.
- D.
- E.
Correct Answer
D.
4.

Fungsi dan ditentukan oleh dan , maka nilai dari
- A.
  
  0
- B.
  
  2
- C.
  
  4
- D.
  
  5
- E.
  
  6
Correct Answer
A. 0
5.

Fungsi dan ditentukan oleh dan , maka nilai dari
- A.
  
  7
- B.
  
  14
- C.
  
  21
- D.
  
  28
- E.
  
  35
Correct Answer
C. 21

Explanation
The given sequence is a multiple of 7, where each number is obtained by multiplying the previous number by 2. Starting with 7, we have 7 * 2 = 14, 14 * 2 = 28, and so on. Therefore, the next number in the sequence would be 35 * 2 = 70. The value of 21 is incorrect.

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1
0
6.

Jika g(x) = 5x + 3 dan (f o g)(x) = 10x + 7, maka nilai f(x) = ....
- A.
  
  2x + 1
- B.
  
  2x - 1
- C.
  
  2x + 2
- D.
  
  2x - 2
- E.
  
  X + 1
Correct Answer
A. 2x + 1

Explanation
The given function composition is (f o g)(x) = 10x + 7. To find the value of f(x), we need to find the inverse of g(x).
Since g(x) = 5x + 3, we can solve for x in terms of g(x):
5x + 3 = g(x)
5x = g(x) - 3
x = (g(x) - 3)/5
Now, substitute this value of x into f(x):
f(x) = 2((g(x) - 3)/5) + 1
f(x) = (2g(x) - 6)/5 + 1
f(x) = (2g(x) - 6 + 5)/5
f(x) = (2g(x) - 1)/5
Therefore, the correct answer is 2x + 1.

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2
0
7.

Fungsi ditentukan oleh , nilai untuk aturan adalah ...
- A.
- B.
- C.
- D.
- E.
Correct Answer
A.
8.

Jika setiap anggota daerah asal pada sebuah fungsi mempunyai pasangan yang berbeda pada daerah kawan, maka fungsi tersebut dinamakan ....
- A.
  
  Fungsi injektif
- B.
  
  Fungsi bijektif
- C.
  
  Fungsi surjektif
- D.
  
  Relasi
- E.
  
  Fungsi domain
Correct Answer
A. Fungsi injektif

Explanation
If every member of the domain of a function has a different pair in the codomain, then the function is called injective.

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9.

Fungsi yang disebut juga dengan korespondensi satu-satu adalah ...
- A.
  
  Fungsi bijektif
- B.
  
  Fungsi onto
- C.
  
  Fungsi into
- D.
  
  Fungsi surjektif
- E.
  
  Fungsi injektif
Correct Answer
A. Fungsi bijektif

Explanation
Fungsi bijektif adalah fungsi yang memiliki sifat korespondensi satu-satu, artinya setiap elemen pada himpunan asal memiliki pasangan unik di himpunan sasaran, dan setiap elemen pada himpunan sasaran memiliki pasangan unik di himpunan asal. Dengan kata lain, setiap elemen pada kedua himpunan terhubung secara unik.

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10.

Diketahui f(x) = 3x + 4 dan g(x) = 2(x - 1). Nilai dari (f + g)(x) = ...
- A.
  
  X + 6
- B.
  
  5x + 2
- C.
  
  5x - 2
- D.
  
  X - 6
- E.
  
  2x + 5
Correct Answer
B. 5x + 2

Explanation
The given question asks for the value of (f + g)(x), which is the sum of the functions f(x) and g(x). To find this sum, we need to add the two functions together.

f(x) = 3x + 4
g(x) = 2(x - 1)

To add these functions, we add the corresponding terms together:
(f + g)(x) = (3x + 4) + (2(x - 1))

Expanding the second term, we get:
(f + g)(x) = 3x + 4 + 2x - 2

Combining like terms, we have:
(f + g)(x) = 5x + 2

Therefore, the correct answer is 5x + 2.

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11.

Diketahui f(x) = 3x + 4 dan g(x) = 2(x - 1). Nilai dari (f - g)(x) = ...
- A.
  
  X + 6
- B.
  
  X - 6
- C.
  
  2x + 6
- D.
  
  2x - 6
- E.
  
  2x + 2
Correct Answer
A. X + 6

Explanation
The given problem involves two functions f(x) and g(x). To find (f - g)(x), we need to subtract g(x) from f(x).

Given f(x) = 3x + 4 and g(x) = 2(x - 1), we can substitute these values into the expression (f - g)(x).

(f - g)(x) = (3x + 4) - (2(x - 1))
= 3x + 4 - 2x + 2
= x + 6

Therefore, the correct answer is x + 6.

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12.

Diketahui f(x) = 3x + 4 dan g(x) = 2(x - 1). Nilai dari (f x g)(x) = ...
- A.
- B.
- C.
- D.
- E.
Correct Answer
A.

Explanation
The given question is asking for the value of (f x g)(x), where f(x) = 3x + 4 and g(x) = 2(x - 1). To find the value of (f x g)(x), we need to substitute g(x) into f(x) and simplify the expression. Substituting g(x) into f(x), we get (f x g)(x) = f(g(x)) = f(2(x - 1)) = 3(2(x - 1)) + 4 = 6x - 6 + 4 = 6x - 2. Therefore, the value of (f x g)(x) is 6x - 2.

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13.

Jika , tentukan nilai dari
- A.
  
  31
- B.
  
  35
- C.
  
  41
- D.
  
  45
- E.
  
  51
Correct Answer
A. 31

Explanation
The given sequence of numbers is 31, 35, 41, 45, 51. The numbers in the sequence are increasing by 4 each time. Starting with 31, adding 4 gives us 35, adding 4 again gives us 39, and so on. However, 39 is not in the sequence, so the next number must be 41. Adding 4 again gives us 45, and adding 4 one more time gives us 49, which is not in the sequence. Therefore, the next number in the sequence is 51.

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14.

Bila , maka f(x + 1) = ...
- A.
- B.
- C.
- D.
- E.
Correct Answer
C.
15.

Bila dan , maka nilai
- A.
  
  32
- B.
  
  38
- C.
  
  41
- D.
  
  43
- E.
  
  46
Correct Answer
E. 46
16.
- A.
  
  13
- B.
  
  25
- C.
  
  37
- D.
  
  49
- E.
  
  81
Correct Answer
D. 49
17.
- A.
  
  7
- B.
  
  9
- C.
  
  11
- D.
  
  14
- E.
  
  17
Correct Answer
C. 11
18.

Diantara relasi di bawah ini yang termasuk fungsi adalah ...
- A.
  
  {(a,1);(a,2);(a,3);(a,4)}
- B.
  
  {(a,1);(b,1);(c,1);(c,2)}
- C.
  
  {(a,1);(b,2);(c,3);(d,4)}
- D.
  
  {(a,1);(b,1);(b,2);(b,3)}
- E.
  
  {(a,1);(b,1);(b,2);(d,1)}
Correct Answer
C. {(a,1);(b,2);(c,3);(d,4)}

Explanation
The given answer {(a,1);(b,2);(c,3);(d,4)} is the only relation that satisfies the definition of a function. In a function, each input element (in this case, the first element of each pair) must have a unique output element (the second element of each pair). In the given answer, each input element (a, b, c, d) has a unique output element (1, 2, 3, 4), satisfying the definition of a function. The other relations in the options either have repeated output elements for the same input element or have different input elements with the same output element, which do not meet the criteria of a function.

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1
0
19.

Range dari fungsi dengan domain adalah ...
- A.
- B.
- C.
- D.
- E.
Correct Answer
B.
20.

Diantara pernyataan berikut yang benar adalah ...
- A.
  
  Setiap relasi pasti merupakan fungsi
- B.
  
  Fungsi adalah relasi
- C.
  
  Setiap fungsi pasti merupakan relasi
- D.
  
  Relasi dan fungsi sama saja
- E.
  
  Semua jawaban benar
Correct Answer
C. Setiap fungsi pasti merupakan relasi

Explanation
Every function is a relation because a function is a specific type of relation where each input has exactly one output. Therefore, the statement "setiap fungsi pasti merupakan relasi" (every function is a relation) is correct.

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