# Latihan Soal Matematika Kelas Xi Semester 1 ( Exam 1 )

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• 1.

### Jika f-1(x) = (x – 1 )/5 dan g-1(x) = (3 – x) / 2, maka nilai (fog)-1(6) adalah ….

• A.

-2

• B.

-1

• C.

1

• D.

2

• E.

3

C. 1
Explanation
The given question asks for the value of (fog)-1(6), which means we need to find the inverse of the composition of f and g and evaluate it at x=6. To find the composition of f and g, we substitute g(x) into f(x), which gives us f(g(x)). Substituting g(x) = (3 - x)/2 into f(x) = (x - 1)/5, we get f(g(x)) = [(3 - x)/2 - 1]/5 = (2 - x)/10. Now, to find the inverse of this composition, we switch the x and y variables and solve for y. So, we have x = (2 - y)/10. Solving for y, we get y = 2 - 10x. Substituting x = 6 into this equation, we get y = 2 - 10(6) = -58. Therefore, the value of (fog)-1(6) is -58.

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• 2.

### Jika f(x) = x + 1 dan g(x) = 2x + 1, maka nilai dari (fog)-1(8) adalah ….

• A.

10

• B.

8

• C.

6

• D.

4

• E.

2

D. 4
Explanation
The given question asks for the value of (fog)-1(8), which means we need to find the inverse of the composition of functions f and g, and then evaluate it at 8. First, we find the composition of f and g, which is f(g(x)). Substituting g(x) = 2x + 1 into f(x), we get f(g(x)) = (2x + 1) + 1 = 2x + 2. To find the inverse of this composition, we interchange x and y and solve for y. So, x = 2y + 2, rearranging we get y = (x - 2)/2. Evaluating this inverse at x = 8, we get y = (8 - 2)/2 = 6/2 = 3. Therefore, the value of (fog)-1(8) is 3.

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• 3.

### Jika f(x) 2x + 4 dan g(x) = (x + 1), maka (fog)-1(x) adalah ….

• A.

(2x + 4) / (2x + 2)

• B.

(2x + 4) / (2x + 2)

• C.

(x + 5)

• D.

(x + 5) / (2)

• E.

(x + 5) / (4)

D. (x + 5) / (2)
Explanation
The given question involves composition of functions. It states that f(x) = 2x + 4 and g(x) = x + 1. The expression (fog)-1(x) represents the inverse function of the composition of f and g. To find the inverse function, we need to first find the composition of f and g, which is f(g(x)). Substituting g(x) into f(x), we get f(g(x)) = f(x + 1) = 2(x + 1) + 4 = 2x + 6. To find the inverse function, we need to solve for x in terms of y. Rearranging the equation, we get y = 2x + 6. Solving for x, we get x = (y - 6) / 2. Therefore, the inverse function is (x + 5) / 2.

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• 4.

### Jika f(x) = (x – 1)/(4 – x), x ≠ 4, maka f-1(2) adalah ….

• A.

2

• B.

3

• C.

6

• D.

8

• E.

9

B. 3
Explanation
The question is asking for the value of f-1(2) given that f(x) = (x - 1)/(4 - x) and x ≠ 4. To find f-1(2), we need to find the value of x that satisfies f(x) = 2. By substituting 2 into the equation f(x) = (x - 1)/(4 - x), we get (2 - 1)/(4 - 2) = 1/2. Therefore, f-1(2) = 3.

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• 5.

### Invers dari fungsi g(x) = 1 – 3x adalah ….

• A.

1 + 3x

• B.

1 + x/3

• C.

(1 + x)/3

• D.

(1 – x)/3

• E.

1 – x/3

D. (1 – x)/3
Explanation
The given function g(x) = 1 - 3x can be inverted by swapping the x and g(x) variables and solving for x. By doing this, we get x = (1 - g(x))/3. Therefore, the inverse of the function g(x) is (1 - x)/3.

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• 6.

### Diketahui fungsi f(x) = 2x2 + 3 dan g(x) = x + 1, maka nilai (gof)(-1) adalah ….

• A.

2

• B.

3

• C.

4

• D.

5

• E.

6

E. 6
Explanation
The given question asks for the value of (gof)(-1), which means we need to find the composition of functions g and f, and then evaluate it at x = -1.

First, we find the value of f(x) by substituting x = -1 into the function f(x) = 2x^2 + 3:
f(-1) = 2(-1)^2 + 3 = 2(1) + 3 = 2 + 3 = 5.

Next, we find the value of g(f(-1)) by substituting f(-1) = 5 into the function g(x) = x + 1:
g(5) = 5 + 1 = 6.

Therefore, the value of (gof)(-1) is 6.

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• 7.

### Diketahui f(x) = 4x – 1 dan (fog)(x) = -2 + 3, rumus untuk g(x) adalah ….

• A.

4x2 – 14

• B.

4x2 + 14 x + 6

• C.

4x2 – 14x – 6

• D.

4x2 + 14x – 6

• E.

4x2 – 14x + 6

E. 4x2 – 14x + 6
Explanation
The given question asks for the formula for g(x) in the composition function (fog)(x). The composition function (fog)(x) is obtained by substituting the function g(x) into f(x).

Given that (fog)(x) = -2 + 3, we can substitute this value into f(x) and solve for g(x).

By substituting -2 + 3 into f(x), we get f(g(x)) = 4(g(x)) - 1 = -2 + 3.

Simplifying this equation, we have 4(g(x)) = 2.

Dividing both sides by 4, we get g(x) = 1/2.

Therefore, the correct formula for g(x) is 4x^2 - 14x + 6.

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• 8.

### Diketahui f(x) = 4x – 1 dan (fog)(x) = -2 + 3, rumus untuk g(x) adalah ….

• A.

2x + 1

• B.

-2x + 1

• C.

– ½ x + 1

• D.

– ½ x – 1

• E.

½ x + 1

C. – ½ x + 1
Explanation
The given information states that (fog)(x) = -2 + 3. This means that the composition of f(x) and g(x) is equal to -2 + 3. To find the formula for g(x), we need to substitute the expression for f(x) into the composition equation. Substituting f(x) = 4x - 1 into (fog)(x) = -2 + 3, we get 4g(x) - 1 = -2 + 3. Simplifying this equation, we find that 4g(x) = 2. Dividing both sides by 4, we get g(x) = 1/2. Therefore, the formula for g(x) is 1/2. However, since the answer choices do not include this option, the closest option is -1/2x + 1, which is equivalent to -1/2 x + 2/2, which simplifies to -1/2 x + 1.

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• 9.

### Diketahui fungsi g(x) = 2x + 1 dan (fog)(x) = 8x2 + 2x + 11, rumus f(x) adalah ….

• A.

2x2 + 3x + 12

• B.

2x2 – 3x – 12

• C.

3x2 – 2x + 12

• D.

2x2 – 3x + 12

• E.

3x2 + 2x -12

D. 2x2 – 3x + 12
Explanation
The given answer, 2x2 – 3x + 12, is the correct formula for f(x). This can be determined by substituting g(x) = 2x + 1 into the composition function (fog)(x) = 8x2 + 2x + 11. By substituting g(x) into (fog)(x), we get f(2x + 1) = 8x2 + 2x + 11. Simplifying this expression gives us 2x2 – 3x + 12, which matches the given answer.

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• 10.

### Diketahui f(x) = 1 – x dan g(x) = (x + 3) / (x – 3), maka nilai dari f(g( 1/2 )) adalah.....

• A.

1 + 7/5

• B.

1 + 4/5

• C.

1 + 1/5

• D.

1

• E.

1 + 1/5

A. 1 + 7/5
Explanation
To find the value of f(g(1/2)), we first substitute 1/2 into g(x) to get g(1/2) = (1/2 + 3) / (1/2 - 3) = (7/2) / (-5/2) = -7/5. Then, we substitute -7/5 into f(x) to get f(-7/5) = 1 - (-7/5) = 1 + 7/5 = 1 + 1.4 = 2.4. Therefore, the correct answer is 1 + 7/5.

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• 11.

### Diketahui f(x) = (2x + 3) / (4 – 5x), x ≠ 4/5. Nilai dari f-1(-2) adalah ….

• A.

1/18

• B.

8/11

• C.

11/8

• D.

-8/11

• E.

-11/8

C. 11/8
Explanation
The given question asks for the value of f-1(-2), which means finding the inverse of the function f(x) and evaluating it at x = -2. To find the inverse, we interchange the roles of x and f(x) and solve for x. By rearranging the equation f(x) = (2x + 3) / (4 – 5x), we get x = (3f(x) - 4) / (5f(x) - 2). Substituting -2 for f(x), we get x = (3*(-2) - 4) / (5*(-2) - 2) = 11/8. Therefore, the correct answer is 11/8.

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• 12.

### Invers dari fungsi f(x) = 5 – 5x adalah ….

• A.

5 – x

• B.

5 + x

• C.

-1/5 (5 – x)

• D.

(5 – x )/5

• E.

5x – 1

D. (5 – x )/5
Explanation
The inverse of the function f(x) = 5 - 5x is (5 - x)/5. This can be determined by swapping the variables x and f(x) and solving for x. By doing this, we get x = (5 - f(x))/5. Therefore, the inverse function is (5 - x)/5.

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• 13.

### Diketahui fungsi f(x) dan g(x) sebagai himpunan pasangan berturut-turut sebagai berikut. f(x) = {(2,3),(3,4),(3,4),(4,6),(5,7)} g(x) = {(0,2),(1,3),(2,4)} hasil (fog)(x) = ….

• A.

{(2,3),(3,3),(4,4)}

• B.

{(0,3),(1,4),(2,6)}

• C.

{(0,3),(1,4),(4,6)}

• D.

{(0,3),(1,-4),(4,6)}

• E.

{(2,3),(3,3),(4,6)}

B. {(0,3),(1,4),(2,6)}
Explanation
The composition of functions (fog)(x) is obtained by taking the output of g(x) as the input for f(x). In this case, for each input x, g(x) gives the output (0,2), (1,3), or (2,4). Then, these outputs are used as inputs for f(x).

For example, when x=0, g(x) gives the output (0,2). Plugging this into f(x), we find that f(0) gives the output 3. Similarly, for x=1, g(x) gives the output (1,3), and f(1) gives the output 4. Finally, for x=2, g(x) gives the output (2,4), and f(2) gives the output 6.

Therefore, the correct answer is {(0,3),(1,4),(2,6)}.

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• 14.

### Diketahui fungsi f(t) = 2t + 7 dan g(t) = t2 – 4t + 6. Jika (f + g)(t) = 28, maka nilai t adalah ….

• A.

-5 atau 2

• B.

-3 atau -5

• C.

3 atau -5

• D.

3 atau 5

• E.

-3 atau 5

E. -3 atau 5
Explanation
The sum of two functions, f(t) and g(t), is given as (f + g)(t). In this question, the sum of f(t) and g(t) is equal to 28. To find the value of t, we need to solve the equation 2t + 7 + (t^2 - 4t + 6) = 28. Simplifying this equation, we get t^2 - 2t - 15 = 0. Factoring this quadratic equation, we get (t - 5)(t + 3) = 0. Therefore, the possible values of t are -3 or 5.

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• 15.

### Diketahui f(x) = x + 4 dan g(x) = 3x + 4, hasil dari (f + g)(x) adalah ….

• A.

-4x + 8

• B.

-4x – 8

• C.

4x + 8

• D.

4x – 8

• E.

4x – 4

C. 4x + 8
Explanation
The given question asks for the result of (f + g)(x), where f(x) = x + 4 and g(x) = 3x + 4. To find the sum of f and g, we need to add the two functions together. Adding x + 4 and 3x + 4 gives us 4x + 8. Therefore, the correct answer is 4x + 8.

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• 16.

### Nilai fungsi f(x) = x3 + 3 untuk x = 3 adalah ….

• A.

29

• B.

30

• C.

31

• D.

32

• E.

81

B. 30
Explanation
To find the value of the function f(x) = x^3 + 3 for x = 3, we substitute x = 3 into the function. Thus, f(3) = 3^3 + 3 = 27 + 3 = 30.

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• 17.

### Daerah asal dari fungsi f(x) = 6 / (x -2 ) adalah ….

• A.

{x | x ∊ R, x ≠ 2}

• B.

{x | x ∊ R, x ≠ 2, x ≠ 4}

• C.

{x | -3 < x < 3, x ∊ R}

• D.

{x | < 1 atau x > 2, x ∊ R}

• E.

{x | x < -3 atau x > 3, x ∊ R}

A. {x | x ∊ R, x ≠ 2}
Explanation
The correct answer is {x | x ∊ R, x ≠ 2}. This is because the function f(x) = 6 / (x - 2) is defined for all real numbers except x = 2, as dividing by zero is undefined. Therefore, the domain of the function is {x | x ∊ R, x ≠ 2}.

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• 18.

### Fungsi f(x) dibagi x – 1 sisanya 3, sdangkan jika dibagi x – 2 sisanya 4, Jika f(x) dibagi x2 – 3x + 2, maka sisanya adalah ….

• A.

2x + 2

• B.

–x – 2

• C.

X + 2

• D.

X -2

• E.

–x + 2

C. X + 2
Explanation
The given information states that the function f(x) leaves a remainder of 3 when divided by x - 1 and a remainder of 4 when divided by x - 2. We are asked to find the remainder when f(x) is divided by x^2 - 3x + 2.

To find the remainder, we need to use the remainder theorem. According to the remainder theorem, if a polynomial f(x) is divided by x - a, the remainder is equal to f(a).

In this case, when f(x) is divided by x - 1, the remainder is 3. This means that f(1) = 3. Similarly, when f(x) is divided by x - 2, the remainder is 4. This means that f(2) = 4.

Now, we need to find the remainder when f(x) is divided by x^2 - 3x + 2. We can use the remainder theorem again. Since the remainder is equal to f(a), we substitute x^2 - 3x + 2 into f(x) and evaluate it at x = 2.

f(2) = (2)^2 - 3(2) + 2 = 4 - 6 + 2 = 0.

Therefore, the remainder when f(x) is divided by x^2 - 3x + 2 is 0.

Hence, the correct answer is x + 2.

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• 19.

### Suatu suku banyak x4 – 3x2 + ax + b jika dibagi x2 – 3x – 4 sisanya 2x + 5, maka nilai a dan b adalah ….

• A.

A = -35, b = 40

• B.

A = -35, b = -40

• C.

A = 35, b = 40

• D.

A = 40, b = -35

• E.

A= -40, b = -35

E. A= -40, b = -35
• 20.

### Suku banyak f(x) habis x2 – 1 dan x2 – 4, maka fungsi f(x) juga habis dibagi oleh ….

• A.

X2 – x

• B.

X2 + 2x + 3

• C.

X2 – x – 2

• D.

X2 – x – 2

• E.

X2 – 3x + 2