S.T. DANIEL COMBONI SECONDARY SCHOOL HAWASSA
2023/24
2016E.C WORK SHEET 1
1989/18. Suppose 𝑓 = { 1,2 , 2,4 , 4,1 , 0,3 , 3,4 } and 𝑔 = { 2,3 , 4,5 , 1,8 , 3,4 , 0,9 }. Then which
of following is NOT true
A.𝑓 + 𝑔 = 1,10 , 2,7 , 4,6 , 0, 12 , 3,8
C. 𝑓 −1 = { 2,1 , 4,2 , 1,4 , 3,0 , 4,3 }
B. 𝑔 − 𝑓 = { 1,6 , 2, −1 , 4,4 , 0, 6 , 3,0 } D. 𝑔𝑜𝑓 = { 1,3 , 2,5 , 3,5 , 4,8 , 0,4 }
E. None of the above
1989/30. The shaded region below is the graph of which of the following relations ?
A. 𝑥, 𝑦 𝑦 ≤ 𝑥 2 − 4 and 𝑦 ≥ 𝑥 + 2 }
C. 𝑥, 𝑦 𝑦 ≥ 𝑥 2 − 4 and 𝑦 ≤ 𝑥 + 2 }
2
B. 𝑥, 𝑦 𝑦 ≥ 𝑥 − 4 and 𝑦 ≥ 𝑥 + 2 }
D. 𝑥, 𝑦 𝑦 ≤ 𝑥 2 − 4 and 𝑦 ≤ 𝑥 + 2 }
E. None of the above
1991/9. Which of the following names can correctly be applied to the function 𝑓 𝑥 = 𝑥 2 ?
A) constant function B) Absolute value function C) Linear function D) Quadratic function
1
1991/10. If 𝑓 𝑥 = 𝑥 − 𝑥 and 𝑥 = 𝑥 , then which of the following is true ?
A) Domain of 𝑓𝑜𝑔 𝑖𝑠 𝑥: 𝑥 ≠ 0
B) Domain of 𝑔𝑜𝑓 𝑖𝑠 𝑥: 𝑥 ≠ 0
C) 𝑓
1
𝑥
= 𝑓 −𝑥 D) 𝑓 𝑥 − 𝑔 𝑥 =
2𝑥 2 −1
𝑥
1991/12. If A = −2, −1,0,1,2 and B = x, y | x ∈ A, y ∈ A and x − y ∈ A , then which of the following is
not true?
A) If x ∈ A, then x, y ∈ B
C) If x, y ∈ B, then (y, x) ∈ B
B)If x ∈ A and y ∈ A, then (x, y) ∈ B D)If x, y ∈ B, then y − x ∈ A
1991/15. Given below is the graph of a relation R. Which of the following is NOT true about the relation R ?
A) Range of 𝑅 = 𝑦 | 0 < 𝑦 < 8
C)𝑅 = 𝑥, 𝑦 | 1 < 𝑥 < 4 𝑎𝑛𝑑 0 < 𝑦 < 8
B) Domain of 𝑅 = 𝑥 | 1 < 𝑥 < 4
D)(3, 5) ∈ 𝑅
1991/37. Let 𝑓 𝑥 = 2𝑥 and 𝑔 𝑥 = 2−𝑥 . Which of the following is NOT true about the unction (𝑓 − 𝑔)(𝑥) ?
A)Its range is 𝑦 ∶ 𝑦 > 0
C) Its graph lies below the 𝑥 − 𝑎𝑥𝑖𝑠 for 𝑥 < 0
B) Its graph passes through the origin
D) It is positive for 𝑥 > 0
𝑎 𝑥 + 𝑎 −𝑥
𝑎 𝑥 − 𝑎 −𝑥
1992/15. If for 𝑎 > 1, 𝑓 𝑥 =
and 𝑔 𝑥 =
, then which of the following is not true ?
2
2
𝑔(𝑥)
A) 𝑓(𝑥) 2 − 𝑔 𝑥 2 = 1 B)𝑔 −𝑥 = −𝑔(𝑥) C)𝑓 𝑥 + 𝑦 + 𝑓 𝑥 − 𝑦 = 2𝑓 𝑥 ∙ 𝑓(𝑦) D)𝑓 𝑥 ∙ 𝑔 𝑥 = 4
1992/25. Which of the following is NOT true ?
A) The range of the inverse of the relation 𝑅 = 𝑥, 𝑦 | 𝑦 > 𝑥 2 𝑎𝑛𝑑 𝑦 ≤ 4 is 𝑦 | − 2 ≤ 𝑦 ≤ 2
B) The domain of the relation 𝑅 = 𝑥, 𝑦 | 𝑥 − 𝑦 < 2 𝑎𝑛𝑑 𝑥 > 0 is 𝑥 | 𝑥 > 0
C) If R is relation on the set of real numbers, then the graph of 𝑅 −1 can be obtained by
reflecting the graph of R along the line 𝑦 = 𝑥
D) A function is a relation
3𝑥 − 1 ,
𝑖𝑓 𝑥 > 3 ,
3
2
1993/36. If 𝑓 𝑥 = 𝑥 − 2, 𝑖𝑓 − 2 ≤ 𝑥 ≤ 3 , then what is 𝑓 − 2 ?
2𝑥 + 3 ,
𝑖𝑓 𝑥 < −2
1
−11
−21
A)4
B) 0
C) 2
D) 4
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1993/22. Below is given the graph of a power function 𝑓 𝑥 = 𝑥 𝑟 . Which of the following is true about r ?
1
A) r is an odd negative integer
B) r is an even negative integer
C) r = 𝑘 , where k is an odd integer
1
D) r = 𝑘 , where k is an even integer different from 0
1993/37. If 𝑓 𝑥 = 𝑥 , 𝑔 𝑥 = 6 − 𝑥, then what is the domain of 𝑓 + 𝑔 𝑥 ?
A) [ 0, ∞)
B) [0,6]
C) (−∞, 6]
D) [0,∞) ∪ (−∞, 6]
1993/38. Let 𝑓: ℝ ⇒ ℝ be defined by 𝑓 𝑥 = 2𝑥 and 𝑔: ℝ ⇒ ℝ be defined by 𝑔 𝑥 = 3𝑥 − 1 . Which of the
following is NOT true ?
A) 𝑓 + 𝑔 is a one to one function.
C) 𝑔0𝑓 𝑥 is an onto function
5
1
B) 𝑓 −1 + 𝑔−1 𝑥 = 6 𝑥 + 3
D) None of the above
1993/52. Let = 𝑥, 𝑦 : 𝑦 < 𝑥 𝑎𝑛𝑑 𝑥 + 𝑦 < 2 . Which of the following statements is true ?
A) The Range of 𝑅 −1 is ( −∞, 1)
C) 1, −3 ∈ 𝑅 −1
B) The Domain of 𝑅 −1 is (−∞, 1)
D) 𝑅 = 𝑅 −1
1993/53. Let A = 0,1 ,2 ,3, 4, 5 . If 𝑅 = 𝑥, 𝑦 : 𝑥 ∈ 𝐴, 𝑦 ∈ 𝐴, 𝑎𝑛𝑑 𝑥 + 𝑦 𝑖𝑠 𝑜𝑑𝑑 ,then which of the
following statements is NOT true ?
A) If 𝑥, 𝑦 ∈ 𝑅 . 𝑡𝑕𝑒𝑛 𝑦, 𝑥 ∈ 𝑅
C) If 𝑥, 𝑦 ∈ 𝑅 𝑡𝑕𝑒𝑛 𝑥 2 . 𝑦 2 ∈ 𝑅
B) If 𝑥, 𝑦 ∈ 𝑅, 𝑎𝑛𝑑 𝑦, 𝑧 ∈ 𝑅, 𝑡𝑕𝑒𝑛 𝑥, 𝑧 ∈ 𝑅
D) None of the above
1993/54. If 𝑓 𝑥 = 𝑎𝑥 + 𝑏 and 𝑓 𝑥 = 4𝑥 − 1 , then which of the following can be possible value of b ?
1
A) – 2
B) −
C) – 1
D) 3
3
1994/4. Which of the following represents the graph of the relation 𝑅 = 𝑥, 𝑦 𝑥 = 𝑦 } ?
A.
C.
B.
D.
𝑥
94/5. If 𝑓 𝑥 = 1 + 𝑥 and 𝑥 = 𝑥 − 1 , then which of the following is true ?
1
A. 𝑔𝑜𝑓 −5 = 2
C. The domain of 𝑔𝑜𝑓 𝑥 = 𝑥 𝑥 ≥ 1}
B. The domain of 𝑓𝑜𝑔 𝑥 = 𝑥 𝑥 > 1}
D. 𝑔𝑜𝑓 𝑥 =
2𝑥 − 1
1+𝑥
1994/14. If 𝑓 = { 2,1 , 4,0 , 6,3 , 8,5 } and = { 2,3 , 4,0 , 6, −2 , 8, −1 } , then
A.
2,
1
3
, 4,0 , 6,
1
−3
−3
2
, (8, −5)
C.
1
1, 3 , 1,
−3
2
𝑓
𝑔
is equal to:
, (1, −5)
B. 2, 3 , 6, 2 , (8, −5)
D. None of the above
𝑥
1994/23. Let 𝑓 𝑥 = 3 . Then which of the following is true for each real number 𝑥 and ?
1
A. 𝑓 𝑥𝑦 = 𝑓 𝑥 𝑓(𝑦) B. 𝑓 𝑥 + 𝑦 = 𝑓 𝑥 + 𝑓(𝑦) C. 𝑓(𝑥 − 1)(𝑓(𝑥)
D. 𝑓 𝑥 2 + 1 = 3 𝑓(𝑥 2 )
1994/26. If 𝑅 = 𝑥, 𝑦 𝑦 2 + 𝑥 = 1}, then which of the following is true ?
A. The range of 𝑅 is the set of all real numbers.
C. (−1,0) belongs to R
B. The domain of R is the set of all real numbers
D. (3,2) belongs to R
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S.T. DANIEL COMBONI SECONDARY SCHOOL HAWASSA
𝑥 +1
1999/9. If 𝑓 𝑥 = 𝑥 − 1 and 𝑓 𝑎 = 5, then 𝑓(2𝑎) is equal to:
𝑥 −8
A. 2
B. 4
2023/24
C. 6
D. 8
𝑥 +2
2001/33. Suppose 𝑥 3 +4𝑥 = 𝑔 𝑥 − 𝑥 2 +4 𝑎𝑛𝑑𝑥 ≠ 0 . Which of the following is equal to 𝑔 𝑥 ?
2𝑥 −1
2𝑥+1
𝑥+2
𝑥−2
A) 𝑥 2 +4
B) 𝑥 2 +4
C) 𝑥 2 +4
D) 𝑥 2 +4
2001/36. Which of the following is the inverse of f 𝑥 = 2 + ln 𝑥 − 1 ?
A) 𝑔 𝑥 = 2 + 𝑒 𝑥−1 B) 𝑔 𝑥 = 1 + 𝑒 𝑥−2
C) 𝑔 𝑥 = 2 − 𝑒 𝑥−1
D) 𝑔 𝑥 = 1 − 𝑒 𝑥−2
2002/5 For Which of the following does its graph lie both above and below the 𝑥 −axis ?
A) 𝑓 𝑥 = 𝑥 + 1 2 2 − 𝑥 2
C) 𝑓 𝑥 = 𝑥 2 + 1 𝑥 − 1 2
B) 𝑓 𝑥 = − 𝑥 = 2 2 𝑥 − 2 2
D) 𝑓 𝑥 = 𝑥 + 1 2 𝑥 2 − 1
2003/2. Which of the following functions touches but never crosses the x- axis ?
A) 𝑓 𝑥 = 1 − 𝑥 3
B) 𝑓 𝑥 = 𝑥 4 − 1
C) 𝑓 𝑥 = 𝑥 2 − 1 2
D) 𝑓 𝑥 = 𝑥 − 𝑥 5
𝑥− 𝑥
2004/1. If 𝑥 < 0, then the simplest form of 𝑓 𝑥 = 𝑥 is equal to: A) 2x B) 2 C) – 2 D) 0
2004/2. If 𝑓 𝑥 =
𝑥 +2
𝑥 +2
1
and 𝑔 𝑥 = 𝑥 − 2 , then 𝑓 𝑔 𝑥
A) 𝑥 − 2
B) 𝑥 + 2
𝑥
2004/3. If 𝑓 𝑥 = 𝑙𝑛
is equal to :
C) 𝑥
D)
𝑥
𝑥
+ 2 , for x> 1, then which one of the following is the inverse of 𝑓 ?
𝑥−1
𝑒 𝑥 −2
A) 𝑔 𝑥 = 𝑒 𝑥 −3
B) 𝑔 𝑥 =
𝑒 𝑥 −2
𝑒 𝑥 +1
𝑒𝑥
C) 𝑔 𝑥 = 𝑒 𝑥 +1 − 2
𝑥
D) 𝑔 𝑥 = 𝑒 𝑥 −1 − 2
2005/31. Given 𝑓 𝑥 = 𝑙𝑛 𝑥 − 1 and g 𝑥 = 1 − 2𝑥 . Which one of the following is the domain of 𝑓𝑜𝑔 ?
1
1
A) 𝑥 ∈ ℝ: 𝑥 > 1 B) 𝑥 ∈ ℝ ∶ 𝑥 ≤ 2
C) 𝑥 ∈ ℝ: 𝑥 < 0
D) 𝑥 ∈ ℝ ∶ 𝑥 > 2
2005/10. What is the value of 𝑥 + 2𝑥 if 𝑥 < 0 ? A) – 3𝑥
B) 3x
C) – 𝑥
1
−1
2005/18. If 𝑓 𝑥 = 𝑒 𝑥 +1 , then which one of the following is equal to 𝑓 𝑥 ?
A) 𝑙𝑛 1 − 𝑥 − 𝑙𝑛 𝑥
B) 𝑒 𝑥 + 1
𝑥 +1
2006/19. If 𝑓 𝑥 = 𝑥 −1 and f 𝑎 = 5 , then 𝑓 2𝑎 is equal to : A) 2
2006/20. If 𝑓 𝑥 =
A) 𝑙𝑛
C) 𝑙𝑛
B) 4
D) x
1
D)
𝑥 +1
C) 6
1
𝑒𝑥
+1
D) 8
3
1 + 𝑒 −𝑥 , which of the following is equal to𝑓 −1 𝑥 ?
1
1
B) 𝑙𝑛 𝑥 3 −1
C) 𝑙𝑛 1 − 𝑥 3
𝑥 3 +1
D) 1 + 𝑒 −𝑥
3
2007/12. Which of the following function is a one –to-one correspondence ?
A) ∶ 𝑅 ′ → ℝ , 𝑓 𝑥 = tan 𝑥 , where 𝑅 ′ is the domain of
C) 𝑕 ∶ 0, ∞ → 0, ∞ , 𝑕 𝑥 = 𝑥 2
𝑥
B) ∶ ℝ → ℝ , 𝑔 𝑥 = 2
D) 𝑟 ∶ 0, ∞ → 0, ∞ , 𝑟 𝑥 = 𝑥 + 5
2𝑥
2007/38. The inverse of the function defined by 𝑔 𝑥 = 𝑥 + 3 is equal to:
2𝑥
3𝑥
𝑥 −3
𝑥+2
A) 𝑔−1 𝑥 = − 𝑥 −3 B) 𝑔−1 𝑥 = − 𝑥 − 2
C) 𝑔−1 𝑥 = − 2𝑥 D) 𝑔−1 𝑥 = − 3𝑥
2008/5. Which of the following function is a one –to-one function ?
A) 𝑓 = 1,6 , 2,7 , 5,6 , 1,8
C) 𝑕: (0, ∞ → ℝ is given by 𝑕 𝑥 = log 𝑥
B) 𝑘: ℝ → ℝ is given 𝑘 𝑥 = 𝑥 − 3
D) : 𝑥, 𝑦 : 𝑥 𝑖𝑠 𝑎 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑎𝑛𝑑 𝑦 𝑖𝑠 𝑕𝑖𝑠 𝑜𝑟 𝑕𝑒𝑟 𝑟𝑎𝑛𝑘
1
2008/32. The inverse of the function 𝑓 𝑥 = 1 + 2 𝑙𝑛 𝑥 − 3 is equal to :
A) 𝑓 −1 𝑥 = −1 + 2𝑒 𝑥 −3
C) 𝑓 −1 𝑥 = −1 + 𝑒 2 𝑥−3
−1
𝑥−1
B) 𝑓 𝑥 = 3 + 2𝑒
D) 𝑓 −1 𝑥 = 3 + 𝑒 2 𝑥−1
2008/46. If 𝑓 𝑥 = 𝑙𝑛 𝑥 + 1 and g 𝑥 = 𝑥 3 + 7 , then what is the domain of 𝑓𝑜𝑔 𝑥 ?
A) −2, ∞
B) −1, ∞
C) [−2 , ∞)
D) ∅
2008/5. Which one of the following is a one-to-one correspondence function from 𝐴 = [0,1] to [1, 2 ] ?
1
A) 𝑓 𝑥 = 𝑥
B) 𝑓 𝑥 = 3 𝑥 3 + 1
C) 𝑓 𝑥 = 2𝑥 + 1
D) 𝑓 𝑥 = 𝑥 2 + 1
2008/35. If 𝑓: 𝐴 → 𝐵 and 𝑔: 𝐵 → 𝐶 are functions, then which of the following is true about the composition
function?
ZERIHUN TSEGAYE
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S.T. DANIEL COMBONI SECONDARY SCHOOL HAWASSA
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A) Domain of 𝑔𝑜𝑓 ⊆ Domain of 𝑓
C) Domain of 𝑔𝑜𝑓 ⊈ Domain of 𝑓
B) Range of 𝑔𝑜𝑓 ⊈Range of 𝑔
D) Range of 𝑔𝑜𝑓 ⊆ Range of 𝑓
2008/36. If the point 3, −2 is on the graph of 𝑦 = 𝑓 𝑥 ,which is on the graph of 𝑦 = 𝑓 −1 𝑥 ?
1
1
A) 3 , −2
B) 3, −1
C) −2, 3
D) 3 , − 2
2009/10 . Which one of the following is the inverse of 𝑓 𝑥 = 8𝑥 3 + 2 ?
1
13
13
A) 𝑓 −1 𝑥 = 8𝑥 3 +2 B) 𝑓 −1 𝑥 = 2 𝑥 − 2
C) 𝑓 −1 𝑥 = 8𝑥 −3 − 2
D) 𝑓 −1 𝑥 = 8 𝑥 − 2
2009/11. Which of the following function is a one –to-one correspondence ?
A) 𝑓: [0, ∞) → ℝ defined by 𝑓 𝑥 = 𝑥
C) 𝑓: ℝ → [0 , ∞) defined by 𝑓 𝑥 = 3𝑥
B) 𝑓: ℝ → [0 , ∞) defined by 𝑓 𝑥 = x 2
D) 𝑓: (0, ∞) → ℝ defined by 𝑓 𝑥 = log 2 𝑥
4
3
2009/12. If 𝑓 𝑥 = 𝑥 and 𝑓𝑜𝑔 𝑥 = 𝑥 , then what is the value of 𝑔 8 ?
3
A) 2
B) 2
C) 2
D) 2 2
2010/10. Which one of the following is true about signum absolute value as greatest integer functions?
A) 𝑥 = ±𝑥 , for all 𝑥 ∈ ℝ
C) 𝑥 = 𝑥 𝑠𝑔𝑛 𝑥 ,for all 𝑥 ∈ ℝ
B) 𝑥 ≤ 𝑥 , for all 𝑥 ≤ 0
D) 𝑠𝑔𝑛 𝑥 ≤ 𝑥 , for all 𝑥 ≥ 0
3𝑥+1
1
2010/33. Let 𝑥 = 𝑥 _−2 , then what is the range of 𝑓 𝑥 ?A) ℝ ∖ 2
B) ℝ C) ℝ ∖ 3
D) ℝ ∖ − 3
1
2010/42 . Let 𝑓 𝑥 = 𝑥 − 𝑥 2 and 𝑔 𝑥 = 𝑥 . Then what is 𝑔 𝑓
A) 𝑥 − 𝑥 2
B)
x2
𝑥 _−1
1
equals to :
𝑥
C)
1
𝑥2
−𝑥
D)
𝑥 −1
𝑥2
2
2011/4 . Which one of the following is equal to 𝑓 𝑥 = 𝑥 + 4 for every 𝑥 ∈ ℝ
A) 𝑔 𝑥 = 𝑥 + 4 B) 𝑔 𝑥 = 𝑥 + 2 C) 𝑔 𝑥 = 𝑥 + 4
𝐷) 𝑔 𝑥 = 𝑥 + 4
1
−1
2011/38. If 𝑓 𝑥 = 𝑎 𝑥 − 𝑏 and 𝑓 𝑥 + 1 = 2 𝑥 + 2 for each ∈ ℝ , then what must be the values of a and b ?
1
A) 𝑎 = 2 𝑎𝑛𝑑 𝑏 = −2
B) 𝑎 = 2 𝑎𝑛𝑑 𝑏 = 2
C) 𝑎 = 1 𝑎𝑛𝑑 𝑏 = 1
D) 𝑎 = 2 𝑎𝑛𝑑 𝑏 = 3
2011/49. If 𝑓 is the greatest integer function and 𝑔 is the absolute value function then what is the value
1
4
of 𝑓𝑜𝑔 2 + 𝑔𝑜𝑓 − 3 ?
A) 1
B) 3
C) -1
D) 2
𝑚
2012/36. The following graph is the graph of the function 𝑦 = 𝑥 𝑛 ,where m and n are positive integers
and 𝑛 ≠ 0 .
Which of the following is true about m and n ?
A) m is odd, n is even and 𝑚 > 𝑛 .
C) m is odd, n is even and 𝑚 < 𝑛
B) m is even, n is odd and 𝑚 < 𝑛 .
D) m is even, n is odd and 𝑚 > 𝑛
2
2012/49. Let 𝑓 𝑥 = 𝑥 + 2 and g 𝑥 = 𝑥 − 1 . What are the domain and the range of the composition of
𝑓 𝑤𝑖𝑡𝑕 𝑔, 𝑓𝑜𝑔 respectively ?
A) ℝ 𝑎𝑛𝑑 [1 , ∞)
B) ℝ 𝑎𝑛𝑑 [0 , ∞)
C) 0 , ∞ 𝑎𝑛𝑑 [1 , ∞)
D) 0 , ∞ 𝑎𝑛𝑑 [0 , ∞)
2012/63. Let 𝑓 𝑥 = 3 − 2𝑥 . What is the range of ?
3
𝑥
𝑥
3
A) 𝑓 −1 𝑥 = 2𝑥 − 3
B) 𝑓 −1 𝑥 = 3 + 2𝑥
C) 𝑓 −1 𝑥 = 2 − 2 D) 𝑓 −1 𝑥 = 2 − 2
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2013/1. What is the domain and range of the function 𝑓 𝑥 = 2𝑥 4 respectively
A) 0 , ∞ 𝑎𝑛𝑑 (0 , ∞)
B) ℝ 𝑎𝑛𝑑 [0 , ∞)
𝐶) 0 , ∞ 𝑎𝑛𝑑 [0 , ∞)
D) 0 , ∞ 𝑎𝑛𝑑 ℝ
2013/2. Which one of the following define a one- to- one function ?
A) 𝑓 = 𝑥 , 𝑦 : 𝑦 = 3𝑥 − 1
C) 𝑓 = 𝑥 , 𝑦 ∶ 𝑦 𝑖𝑠 𝑎 𝑓𝑎𝑡𝑕𝑒𝑟 𝑜𝑓 𝑥
B) 𝑓 = 𝑥 , 𝑦 ∶ 𝑥 𝑖𝑠 𝑎 𝑠𝑖𝑠𝑡𝑒𝑟 𝑜𝑓 𝑦
D) 𝑓 = 𝑥 , 𝑦 : 𝑦 = x 2 + 1
ZERIHUN TSEGAYE
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S.T. DANIEL COMBONI SECONDARY SCHOOL HAWASSA
2023/24
2013/15. The inverse of the function 𝑦 = 3𝑥 − 5 is equal to :
𝑥+ 3
𝑥+ 5
𝑥 −5
A) 𝑦 = 5
B) 𝑦 = 3
C) 𝑦 = −5𝑥 + 3
D) 𝑦 = 3
2014/1. Let 𝑅 = { 𝑥, 𝑦 ∶ 𝑦 ≥ 𝑥 2 + 1 and 𝑦 ≤ 5} be a relation. Then which one of the following defines the
inverse of R ?
A. 𝑥, 𝑦 𝑥 ≥ 𝑦 2 + 1, 𝑥 ≤ 5}
C. { 𝑥, 𝑦 ∶ 𝑥 ≤ 𝑦 2 + 1, 𝑥 ≥ 5}
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B. 𝑥, 𝑦 𝑥 ≥ 𝑦 + 1, 𝑥 ≥ 5}
D. { 𝑥, 𝑦 ∶ 𝑥 ≥ 𝑦 2 − 1, 𝑥 ≤ 5}
2014/39. Which one of the following is an onto function from ℝ onto [0, ∞) ?
A. 𝑓 𝑥 = 𝑥 2
B. 𝑓 𝑥 = 𝑥 + 2
C. 𝑓 𝑥 = 𝑥 2 + 1
D. 𝑓 𝑥 = 2𝑥
2014/47. The graph of a certain if relation ℝ is represented by the shaded region shown on the figure
below. Which one of the following pairs of sets respectively gives the domain and ranges of this relation ?
A. 𝑥: 𝑥 ≤ 2 and 𝑦: 𝑦 ≤ 6
B. {𝑥 ∶ 𝑥 ≤ 2} and ℝ
C. ℝ and {𝑦 ∶ 𝑦 ≤ 2}
D. ℝ and ℝ
3𝑥 + 1
2014/24. Let 𝑓 𝑥 = 𝑥 + 2 . Which one of the following is the inverse of f ?
𝑥 +2
𝑥 −2
−2𝑥 + 1
2𝑥 − 1
A. 𝑓 −1 𝑥 = 3𝑥 + 1 B. 𝑓 −1 𝑥 = −3𝑥 − 1
C. 𝑓 −1 𝑥 = 𝑥 − 3 D. 𝑓 −1 𝑥 = 𝑥 − 3
2014/11. Let 𝑓 𝑥 = 𝑥 2 − 𝑥 and 𝑔 𝑥 = 𝑥 + 1. Which one of the following statements is true ?
𝑓
A. 𝑔 −2 = −6 B. 𝑓 ∙ 𝑔 −2 = −5 C. 𝑓 − 𝑔 −2 = 5
D. 𝑓 + 𝑔 −2 = 3
2014/18. Which one of the following is true about the signum function 𝑓 𝑥 = 𝑠𝑔𝑛(𝑥) ?
A. Its range is 0, ∞ B. Its domain is {−1,0,1 C. Its range the set of real number D. Its domain is the set of real numbers
2015/1. Given 𝐴 = {𝑥 ∈ ℕ ∶ 𝑥 < 3} an B is the set of all possible factor of 13. Then which one of the
following is equal to 𝐵 × 𝐴 ?
A. { 1,1 , 1,2 , 13,1 , 13,2 } B. { 1,1 , 2,1 , 1,13 , 2,13 } C. { 1,2 , 13,1 , 13,2 } D. { 1,1 , 13,2 }
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2015/ 10. The domain of the function 𝑓 𝑥 = 2𝑥 3 ? A. [0, ∞) B. ℝ \{0} C. (0,2) D. ℝ
2015/25. Which of the following function is one to one ?
A. 𝑓 ∶ 0, ∞ → ℝ, 𝑓 𝑥 = 𝑥 − 1
C. 𝑓 = { 𝑥, 𝑦 ∶ 𝑦 is the mother of 𝑥}
B. 𝑓 = { 1,5 , 2,3 , 5,4 , 6,5 }
D. 𝑓 ∶ ℝ → ℝ, 𝑓 𝑥 = 𝑥 2 − 1
2015/ 6. Which one of the following pairs of functions 𝑓 and 𝑔 are inverses of each other ?
5
A. 𝑓 𝑥 = 5𝑥 and 𝑔 𝑥 = log 𝑥 5
C. 𝑓 𝑥 = 𝑥 + 11 and 𝑔 𝑥 = 𝑥 5 + 11
2𝑥 − 1
3𝑥 + 1
B. 𝑓 𝑥 = 𝑥 + 3 , 𝑥 ≠ −3 and 𝑔 𝑥 = 2 − 𝑥 , 𝑥 ≠ 2
D. 𝑓 𝑥 = (𝑥 − 13)2 and 𝑔 𝑥 = 𝑥 + 13
2015/34. Which one of the following is true about a function 𝑓 defined by 𝑓 𝑥 =
A. Domain of 𝑓 is 𝑥 ∈ ℝ 𝑥 ≥ 7}
B. Range of 𝑓 is 𝑓 𝑥 ∈ ℝ 𝑓(𝑥) ≥ 1}
ZERIHUN TSEGAYE
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5𝑥 − 7
?
C. Range of 𝑓 is 𝑓 𝑥 ∈ ℝ 𝑓 𝑥 > 0}
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D. Domain of 𝑓 is 𝑥 ∈ ℝ | 𝑥 ≥ 5
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