Here are 100 multiple-choice questions (MCQs) on the topic of Functions for IIT JEE (Advanced) exam preparation:
* Key is at the bottom
Functions for IIT JEE (Advanced)
1. The domain of the function f(x) = √(4 - x²) is:
a) (-∞, -2] U [2, ∞)
b) [-2, 2]
c) (-∞, 2] U [2, ∞)
d) [-∞, ∞)
2. If f(x) = x² - 3x + 2 and g(x) = 2x - 1, then the composite function (f ∘ g)(x) is equal to:
a) 2x² - 6x + 3
b) 2x² - 7x + 5
c) 2x² - 7x + 3
d) 2x² - 5x + 3
3. The inverse of the function f(x) = 2x + 3 is:
a) f⁻¹(x) = (x - 3)/2
b) f⁻¹(x) = (x + 3)/2
c) f⁻¹(x) = (x - 3)/4
d) f⁻¹(x) = (x + 3)/4
4. The number of onto functions from a set A with 3 elements to a set B with 4 elements is:
a) 12
b) 24
c) 81
d) 64
5. The range of the function f(x) = |x - 2| + |x + 1| is:
a) (-∞, -3] U [2, ∞)
b) [-2, 2]
c) [-3, 2]
d) [2, ∞)
6. The function f(x) = 2x - 3 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
7. If f(x) = x³ + x and g(x) = x² - 1, then the composite function (g ∘ f)(x) is equal to:
a) x⁵ + x² - 1
b) x⁶ + x³ - 1
c) x⁶ + x² - 1
d) x⁵ + x³ - 1
8. The number of one-one functions from a set A with 5 elements to a set B with 3 elements is:
a) 60
b) 120
c) 243
d) 125
9. The function f(x) = (x - 1)² - 4 is increasing on the interval:
a) (-∞, 1)
b) [1, ∞)
c) (-∞, 3)
d) (3, ∞)
10. The function f(x) = log₄(x + 1) is defined for:
a) x > -1
b) x > 1
c) x ≥ -1
d) x ≥ 1
11. If f(x) = x³ - 3x² + 2x + 1 and g(x) = x + 2, then the composite function (f ∘ g)(x) is equal to:
a) x³ + 5x² + 8x + 9
b) x³ + 5x² + 7x + 5
c) x³ + 7x² + 5x + 5
d) x³ + 7x² + 8x + 9
12. The number of functions from a set A with 3 elements to a set B with 2 elements is:
a) 2
b) 3
c) 6
d) 8
13. The function f(x) = |x - 3| is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
14. The function f(x) = 3x² + 2x - 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
15. The number of onto functions from a set A with 4 elements to a set B with 4 elements is:
a) 24
b) 256
c) 81
d) 64
16. The function f(x) = 5x + 2 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
17. If f(x) = x³ + 1 and g(x) = √x, then the composite function (g ∘ f)(x) is equal to:
a) (x³ + 1)⁻²
b) (x³ + 2)⁻²
c) (x³ + 1)²
d) √(x³ + 1)
18. The inverse of the function f(x) = 3x - 2 is:
a) f⁻¹(x) = (x + 2)/3
b) f⁻¹(x) = (x - 2)/3
c) f⁻¹(x) = (x - 2)/6
d) f⁻¹(x) = (x + 2)/6
19. The function f(x) = log₄(x - 1) is defined for:
a) x > 1
b) x > 0
c) x ≥ 1
d) x ≥ 0
20. The domain of the function f(x) = 1/(√(x - 2)) is:
a) (-∞, 2)
b) [2, ∞)
c) (-∞, 2]
d) [2, ∞)
21. If f(x) = 2x - 1 and g(x) = x + 3, then the composite function (g ∘ f)(x) is equal to:
a) 2x + 5
b) 4x - 2
c) 2x + 1
d) 2x + 7
22. The function f(x) = x² + 2 is increasing on the interval:
a) (-∞, 0)
b) [0, ∞)
c) (-∞, 2)
d) (2, ∞)
23. The number of one-one functions from a set A with 4 elements to a set B with 5 elements is:
a) 120
b) 102
4
c) 625
d) 256
24. The function f(x) = √(x - 1) is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
25. The function f(x) = x³ - 2x² + 3x - 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
26. The number of functions from a set A with 2 elements to a set B with 3 elements is:
a) 3
b) 2
c) 6
d) 8
27. The function f(x) = |x + 1| is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
28. The function f(x) = 4x² + 2x - 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
29. The number of onto functions from a set A with 3 elements to a set B with 3 elements is:
a) 6
b) 27
c) 81
d) 64
30. The function f(x) = 6x + 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
31. If f(x) = x⁴ + 1 and g(x) = √(x + 1), then the composite function (g ∘ f)(x) is equal to:
a) √(x⁴ + 2)
b) (x⁴ + 2)⁻²
c) √(x⁴ + 1)
d) (x⁴ + 1)⁻²
32. The inverse of the function f(x) = 4x + 3 is:
a) f⁻¹(x) = (x - 3)/4
b) f⁻¹(x) = (x + 3)/4
c) f⁻¹(x) = (x + 3)/8
d) f⁻¹(x) = (x - 3)/8
33. The function f(x) = log₄(x + 2) is defined for:
a) x > -2
b) x > -1
c) x ≥ -2
d) x ≥ -1
34. The domain of the function f(x) = √(4 - x) is:
a) (-∞, -4] U [4, ∞)
b) [-4, 4]
c) (-∞, 4] U [4, ∞)
d) [-∞, ∞)
35. If f(x) = 2x + 1 and g(x) = x - 2, then the composite function (g ∘ f)(x) is equal to:
a) 2x - 3
b) 3x + 1
c) 2x - 1
d) 2x + 3
36. The function f(x) = x² - 4 is increasing on the interval:
a) (-∞, -2)
b) [-2, ∞)
c) (-∞, 2)
d) (2, ∞)
37. The number of one-one functions from a set A with 3 elements to a set B with 4 elements is:
a) 12
b) 64
c) 81
d) 256
38. The function f(x) = 2 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
39. The function f(x) = √(x + 2) is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
40. The number of functions from a set A with 5 elements to a set B with 3 elements is:
a) 243
b) 125
c) 32
d) 256
41. The function f(x) = |x - 1| is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
42. The function f(x) = x³ + 2x² - 3x + 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
43. The number of onto functions from a set A with 4 elements to a set B with 5 elements is:
a) 1024
b) 625
c) 2401
d) 256
44. The function f(x) = x² + 3x + 2 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
45. The function f(x) = 7x + 2 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
46. The inverse of the function f(x) = 5x - 3 is:
a) f⁻¹(x) = (x + 3)/5
b) f⁻¹(x) = (x - 3)/5
c) f⁻¹(x) = (x - 3)/10
d) f⁻¹(x) = (x + 3)/10
47. The function f(x) = log₄(x - 2) is defined for:
a) x > 2
b) x > 1
c) x ≥ 2
d) x ≥ 1
48. The domain of the function f(x) = 1/(√(x + 2)) is:
a) (-∞, -2)
b) [-2, ∞)
c) (-∞, -2]
d) [2, ∞)
49. If f(x) = x² + 2 and g(x) = 2x + 1, then the composite function (g ∘ f)(x) is equal to:
a) 2x² + 4x + 1
b) 2x² + 6x + 5
c) 2x² + 5x + 4
d) 2x² + 5x + 1
50. The function f(x) = 3√(
x - 1) is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
51. The number of one-one functions from a set A with 4 elements to a set B with 3 elements is:
a) 81
b) 64
c) 27
d) 256
52. The function f(x) = 3x - 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
53. If f(x) = x⁵ + 1 and g(x) = √(x - 1), then the composite function (g ∘ f)(x) is equal to:
a) √(x⁵ + 2)
b) (x⁵ + 2)⁻²
c) √(x⁵ + 1)
d) (x⁵ + 1)⁻²
54. The inverse of the function f(x) = 2x + 5 is:
a) f⁻¹(x) = (x - 5)/2
b) f⁻¹(x) = (x + 5)/2
c) f⁻¹(x) = (x + 5)/4
d) f⁻¹(x) = (x - 5)/4
55. The function f(x) = log₄(x - 2) is defined for:
a) x > 2
b) x > 1
c) x ≥ 2
d) x ≥ 1
56. The domain of the function f(x) = √(4 - x) is:
a) (-∞, -4] U [4, ∞)
b) [-4, 4]
c) (-∞, 4] U [4, ∞)
d) [-∞, ∞)
57. If f(x) = 2x + 3 and g(x) = x - 2, then the composite function (g ∘ f)(x) is equal to:
a) 2x - 1
b) 3x + 1
c) 2x + 1
d) 2x + 5
58. The function f(x) = x² + 2 is increasing on the interval:
a) (-∞, 0)
b) [0, ∞)
c) (-∞, -2)
d) (-2, ∞)
59. The number of one-one functions from a set A with 2 elements to a set B with 3 elements is:
a) 6
b) 3
c) 8
d) 2
60. The function f(x) = |x + 2| is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
61. The function f(x) = 5x² + 3x - 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
62. The number of onto functions from a set A with 3 elements to a set B with 4 elements is:
a) 12
b) 81
c) 64
d) 256
63. The function f(x) = x³ - 3x is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
64. The function f(x) = 4x² + 2x - 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
65. The number of functions from a set A with 5 elements to a set B with 2 elements is:
a) 2
b) 3
c) 8
d) 6
66. The function f(x) = |x - 2| is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
67. The function f(x) = x² + 3x + 2 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
68. The number of onto functions from a set A with 4 elements to a set B with 5 elements is:
a) 24
b) 1024
c) 625
d) 2401
69. The function f(x) = 7x + 2 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
70. The function f(x) = √(x - 1) is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
71. The number of functions from a set A with 2 elements to a set B with 3 elements is:
a) 3
b) 2
c) 6
d) 8
72. The function f(x) = |x + 1| is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
73. The function f(x) = x³ + 2x² - 3x + 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
74. The number of onto functions from a set A with 3 elements to a set B with 3 elements is:
a) 6
b) 81
c) 64
d) 27
75. The function f(x) = x² + 2x + 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
76. The function f(x) = 5√x is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
77. The inverse of the function f(x) = 3x + 4 is:
a) f⁻¹(x) = (x - 4)/3
b) f⁻¹(x) = (x + 4)/3
c) f⁻¹(x) = (x + 4)/6
d) f⁻¹(x) = (x - 4)/6
78. The function f(x) = log₄(x + 3) is defined
for:
a) x > -3
b) x > -1
c) x ≥ -3
d) x ≥ -1
79. The domain of the function f(x) = 1/(√(x - 2)) is:
a) (-∞, 2)
b) [2, ∞)
c) (-∞, 2]
d) [2, ∞)
80. If f(x) = x² - 1 and g(x) = √(x + 2), then the composite function (g ∘ f)(x) is equal to:
a) √(x² - 1)
b) √(x² - 3)
c) x² - 1
d) x² - 3
81. The function f(x) = 2x - 3 is increasing on the interval:
a) (-∞, 1)
b) [1, ∞)
c) (-∞, 3)
d) (3, ∞)
82. The number of one-one functions from a set A with 4 elements to a set B with 5 elements is:
a) 120
b) 243
c) 125
d) 102
83. The function f(x) = 2 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
84. The function f(x) = √(x + 3) is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
85. The number of functions from a set A with 5 elements to a set B with 3 elements is:
a) 243
b) 125
c) 32
d) 256
86. The function f(x) = 3√(x - 1) is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
87. The function f(x) = x³ + 1 is increasing on the interval:
a) (-∞, 0)
b) [0, ∞)
c) (-∞, -1)
d) (-1, ∞)
88. The number of onto functions from a set A with 3 elements to a set B with 4 elements is:
a) 12
b) 81
c) 64
d) 27
89. The function f(x) = 4x + 2 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
90. The function f(x) = √x is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
91. The number of functions from a set A with 2 elements to a set B with 3 elements is:
a) 3
b) 2
c) 6
d) 8
92. The function f(x) = |x - 2| is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
93. The function f(x) = x³ + 2x² - 3x + 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
94. The number of onto functions from a set A with 3 elements to a set B with 3 elements is:
a) 6
b) 81
c) 64
d) 27
95. The function f(x) = x² + 2x + 1 is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
96. The function f(x) = 5√x is:
a) An even function
b) An odd function
c) Neither even nor odd
d) Constant function
97. The inverse of the function f(x) = 3x + 4 is:
a) f⁻¹(x) = (x - 4)/3
b) f⁻¹(x) = (x + 4)/3
c) f⁻¹(x) = (x + 4)/6
d) f⁻¹(x) = (x - 4)/6
98. The function f(x) = log₄(x + 3) is defined for:
a) x > -3
b) x > -1
c) x ≥ -3
d) x ≥ -1
99. The domain of the function f(x) = 1/(√(x - 2)) is:
a) (-∞, 2)
b) [2, ∞)
c) (-∞, 2]
d) [2, ∞)
100. If f(x) = x² - 1 and g(x) = √(x + 2), then the composite function (g ∘ f)(x) is equal to:
a) √(x² - 1)
b) √(x² - 3)
c) x² - 1
d) x² - 3
Note: Please keep in mind that the answers provided are for reference purposes and it is advised to verify the solutions independently.
KEY
- Certainly! Here's the answer key for the MCQs on the topic of Functions:
1. a) (-∞, -2] U [2, ∞) 2. a) 2x² - 6x + 3
3. b) f⁻¹(x) = (x + 3)/2 4. c) 81
5. a) (-∞, -3] U [2, ∞) 6. c) Neither even nor odd
7. c) x⁶ + x² - 1 8. d) 125
9. b) [1, ∞) 10. a) x > -1
11. d) x³ + 7x² + 8x + 9 12. d) 8
13. c) Neither even nor odd 14. c) Neither even nor odd
15. b) 256 16. c) Neither even nor odd
17. d) √(x³ + 1) 18. a) f⁻¹(x) = (x - 2)/3
19. a) x > 1 20. b) [2, ∞)
21. c) 2x + 1
22. b) [0, ∞)
23. c) 81
24. a) An even function
25. c) Neither even nor odd
26. d) 8
27. b) An odd function
28. c) Neither even nor odd
29. d) 256
30. c) Neither even nor odd
31. c) √(x⁴ + 1)
32. a) f⁻¹(x) = (x - 3)/4
33. a) x > 2
34. c) (-∞, 4] U [4, ∞)
35. c) 2x + 1
36. b) [-2, ∞)
37. a) 12
38. d) Constant function
39. b) An odd function
40. c) 32
41. b) An odd function
42. c) Neither even nor odd
43. c) 625
44. a) An even function
45. d) Constant function
46. a) f⁻¹(x) = (x + 3)/5
47. a) x > 1
48. b) [2, ∞)
49. d) 2x² + 5x + 1
50. a) An odd function
51. c) 27
52. c) Neither even nor odd
53. a) √(x⁵ + 2)
54. b) f⁻¹(x) = (x + 5)/2
55. d) x ≥ 1
56. a) (-∞, -4] U [4, ∞)
57. b) 3x + 1
58. c) (-∞, -2)
59. c) 8
60. a) An odd function
61. c) Neither even nor odd
62. b) 1024
63. b) An odd function
64. c) Neither even nor odd
65. c) 32
66. a) An even function
67. c) Neither even nor odd
68. a) 24
69. b) An odd function
70. a) An even function
71. c) 6
72. b) An odd function
73. c) Neither even nor odd
74. a) 6
75. a) An even function
76. b) An odd function
77. a) f⁻¹(x) = (x - 4)/3
78. b) x > -1
79. b) [2, ∞)
80. c) x² - 1
81. b) [1, ∞)
82. a) 120
83. d) Constant function
84. b) An odd function
85. c) 32
86. b) An odd function
87. b) [0, ∞)
88. a) 12
89. d) Constant function
90. b) An odd function
91. c) 6
92. b) An odd function
93. c) Neither even nor odd
94. a) 6
95. a) An even function
96. b) An odd function
97. a) f⁻¹(x) = (x - 4)/3
98. b) x > -1
99. b) [2, ∞)
100. c) x² - 1
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