For: - 11th, 12th, JEE (Mains + Advance) & NEET

Class : 12th Topic : Function

-: Objective Questions :-
7. If f:R→R,f(x)=x2+1then pre-image of 4 under
1. Which of the following relation is a function? f is-
a. {(1,4),(2,6),(1,5),(3,9)}
a. {√3}
b. {(3,3),(2,1),(1,2),(2,3)}
c. {(1,2),(2,2),(3,2),(4,2)} b. {-√3}
d. {(3,1),(3,2),(3,3),(3,4)} c. {√3, −√3}
2. If x,y Є R,then which of the following rules is d. None of these
not a function- 8. If f:R→R,f(x)=x2+2then pre-image of 1 under
a. Y=9-x2 f is-
b. Y=2x2 a. {1}
c. Y=√𝑥 − |𝑥| b. {-1}
d. Y=x2-1 c. {1,-1}
3. If A and B are two sets such that A={1,2,3} d. None of these
and B={5,7,9} and if a function is defined 9. If f:R→R,f(x)=x2+3 then pre-image of 2 under
from f: A→B,f(x)=2x+3 then find a function f is-
in the form of ordered pairs. a. {-1,1}
a. {(1,5),(2,7),(3,9)} b. {1}
b. {(1,5),(2,6),(3,9)} c. {-1}
c. {(1,5),(2,7),(3,3)} d. ∅
d. {(1,4),(2,6),(3,9)} 10. Find the domain of the function f(x)=x-1
4. Which of the following relation is a function? a. R
a. {(4,1),(5,1),(6,7)} b. R+
b. {(2,3),(2,5),(3,3),(6,6)} c. R-
c. {(1,2),(2,3),(3,4),(4,5),(5,6)(6,7)} d. None of these
d. {(1,1),(2,1),(3,1),(4,1)(5,1)} 11. Find the domain of the function f(x)=x2 +x-1
5. Which of the following relation is a function? a. R
a. {(2,),(2,2),(2,3),(2,4)} b. R+
b. {(1,4),(2,5),(1,6),(3,9)} c. R-
c. {(1,2),(3,3),(2,3),(1,4)} d. None of these
d. {(1,2),(2,2),(3,2),(4,2)} 12. Find the domain of the function f(x)=x2-5x+6
6. If f:R→R,f(x)=tanx, then pre-image of a. R
−1 under f is- b. R+
c. R-
a. {𝑛𝜋 − 𝛱/4│𝑛𝜖𝐼}
d. None of these
b. {𝑛𝜋 + 𝛱/4│𝑛𝜖𝐼} 13. Find the domain of the function f(x)=1/x-1
c. {𝑛𝜋│𝑛𝜖𝐼} a. R b. R0
d. None of these c. R-{1} d. None of these
In front of Tileshwarnath Mandir, Near SBI Chowk, Patna City (9386487790, 7903070219, 8248700030)
14. Find the domain of the function 23. Find the domain of the function f(x)=√1 − 𝑥
f(x)=1/ x2-5x+6 a. (-∞,1]
a. R b. [-1,1]
b. R-{2} c. [1,∞)
c. R-{3} d. (-∞,1)
d. R-{2,3} 24. Find the domain of the function
15. Find the domain of the function f(x)=1/√𝑥 − 1
f(x)=1/x2 +x-1 a. (1,∞)
a. R b. [1,∞)
b. R-{2} c. (-1,1)
c. R-{1} d. [-1,1]
d. None of these
25. Find the domain of the function f(x)=√4 − 𝑥 2
16. Find the domain of the function f(x)=1/x
is
a. R
a. (-∞,-2]U[2,∞)
b. R0
b. (-2,2)
c. R+
c. [-2,2]
d. None of these
d. None of these
17. Find the domain of the function f(x)=x-1/x+2
26. Find the domain of the function
a. R-{2}
f(x)=1/√𝑥 2 − 3𝑥 + 2 is
b. R-{3}
a. (-∞,1)
c. R-{-2}
b. (2,∞)
d. R
c. (-∞,1)U(2,∞)
18. Find the domain of the function
d. (1,2)
f(x)=2x-3/x2-3x+2
a. R-{1} 27. Find the domain of the function f(x)=1/√𝑥 + 2
b. R-{2} is-
c. R-{1,2} a. R
d. None of these b. (-2,∞)
19. Find the domain of the function f(x)=1/x3-x c. [2,∞]
a. R-{-1,0,1} d. [0,∞)
b. R 28. Find the domain of the function
c. R-{0,1} f(x)=√2 − 2𝑥 − 𝑥 2 is-
d. None of these a. -√3 ≤ 𝑥 ≤ √3
2
20. Find the domain of the function f(x)=x/x +1 b. -1-√3 ≤ 𝑥 ≤ −1 + √3
a. R c. -2≤x≤2
b. R-{1} d. -2+√3 ≤ 𝑥 ≤ −2 − √3
c. R-{-1} 29. Find the domain of the function
d. R-{-1,1} f(x)=𝑥 − 3/(𝑥 − 1)√𝑥 2 − 4 is
21. Find the domain of the function f(x)=x2-4/x-2 a. (1,2)
a. R b. (-∞,-2)U(2,∞)
b. R-{2} c. (-∞,-2)U(1,∞)
c. R-{-2} d. (-∞,∞)U(1,±2)
d. R-{-2,2}
22. Find the domain of the function f(x)=√𝑥 − 1
a. R-(-1,1) b. [1,∞)
c. (-∞,1] d. None of these
In front of Tileshwarnath Mandir, Near SBI Chowk, Patna City (9386487790, 7903070219, 8248700030)
30. Find the domain of the function 38. Find the domain of the function f(x)=√𝑥 − |𝑥|
f(x)=√𝑥 2 − 1+√𝑥 2+ 1 is is-
a. 1˂x˂∞ a. [0,∞)
b. -∞˂x˂∞ b. (0,∞)
c. -∞˂x˂-1 c. R
d. (-∞,∞)-(-1,1) d. None of these
1
31. If f(x)=x2-3x+1 and g(x)=𝑥−2 , then domain of 39. Find the domain of the function
(f-g)is- f(x)=1/√𝑥 − |𝑥| is-
a. R a. [0,∞)
b. R+ b. (0,∞)
c. R-{2} c. ∅
d. None of these d. None of these
32. Find the domain of the function 40. Find the domain of the function
f(x)=√𝑥 − 1 +√6 − 𝑥 is f(x)=log 2 (𝑥 + 1) is-
a. (1,6) a. (1,∞)
b. [1,6] b. [1,∞)
c. [1,∞) c. [-1,1]
d. (-∞,6] d. None of these
33. If x is the radius of a circle andf(x)= 𝜋x2, then 41. Find the domain of the function
domain of f is- f(x)=log10 log10 log10 𝑥
a. R a. (1,∞)
b. R+ b. [1,∞)
c. R- c. (-1,1)
d. R0 d. (10,∞)
34. The domain of the function f(x )= x! is 42. Find the domain of the function
a. (0,∞) f(x)=log 2 log 3 log 4 𝑥
b. N a. (4,∞)
c. W b. [4,∞)
d. R+ c. [2,4]
35. If f(x)=1/x+1 and g(x)=1/√𝑥 − 1,then d. (2,3]
common domain of function is- 43. Find the domain of the function
a. {x/x<1,xϵR} f(x)=log 2 (𝑥 + 3)/x2+3x+2
b. {x/x≥0,x≠1,xϵR} a. (-3,∞)
c. {1} b. (-3,∞)-{-1}
d. {-1} c. (-3,∞)-{-2}
36. Find the domain of the function d. (-3,∞)-{-1,-2}
44. Find the domain of the function
f(x)=x-3/(x-1)√𝑥 + 2 is-
f(x)=log 3+𝑥 (𝑥 2 − 1) is-
a. R-(-2,2)
a. (-3,-2)
b. R-[-2,2]
b. (-3,-2) U(-2,-1)
c. (-2,2)
c. (-3,-2) U(-2,-1)U(1,∞)
d. [-2,2]
d. None of these
37. The domain where function f(x)=2x2-1 and
g(x)=1-3x are equal is-
a. {1/2} b. {2}
c. {1/2,2} d. {1/2,-2}
In front of Tileshwarnath Mandir, Near SBI Chowk, Patna City (9386487790, 7903070219, 8248700030)
45. Find the domain of the function 52. Find the domain of the function
5𝑥−𝑥 2 𝑥−1 1
f(x)=log √ is- f(x)=√log 0.4 𝑥+5 .𝑥 2 −36
6
a. (0,5) a. (1,∞)
b. [0,5] b. (1,∞)-{-6}
c. (0,5] c. (1,∞)-{6}
d. [0,5) d. (1,∞)-{-6,6}
46. Find the domain of the function 3−𝑥
53. Find the domain of the function f(x)=log √
5𝑥−𝑥 2 2
f(x)=√log 6 a. (3,∞)
a. (0,5) b. (-∞,3)
b. [0,5] c. (0,3)
c. (2,3) d. (-3,3)
d. [2,3] 54. Find the domain of the function
47. Find the domain of the function f(x)=log( 3𝑥 − 1) + 2 log(𝑥 + 1) is
3𝑥−𝑥 2 a. [1/3,∞)
f(x)=√log 2 b. [-1,1/3]
a. [1,2) c. (-1,1/3)
b. (1,2] d. None of these
c. (1,2) √4−𝑥 2
55. Find the domain of the function 𝑠𝑖𝑛 log
d. [1,2] 1−𝑥

48. Find the domain of the function a. (1,2)

f(x)=log|𝑥 2 − 9| b. (-2,2)
c. (-2,1)
a. R
b. R-{3} d. [-2,1]
c. R-{-3,3} 56. Find the domain of the function sin−1 4𝑥
d. None of these a. [-1,1]
49. Find the domain of the function b. [-1/4,1/4]
f(x)=log|log 𝑒 𝑥| c. (-1,1)
a. (0,1) d. (-1/4,1/4)
b. (0,1)U(1,∞) 57. Find the domain of the function
c. (1,∞] cos−1 (4𝑥 − 1)
d. None of these a. (0,1/2)
50. Find the domain of the function b. [0,1/2]
c. (-1/2,1/2)
𝑥−1
f(x)=√log 0.4 𝑥+5 d. [-1/2,1/2]
a. (-5,∞) 58. Find the domain of the function sin−1 √𝑥
b. (1,∞ ) a. (0,1)
c. (-∞,-5)U(1,∞) b. {0,1}
d. (-∞,-5)U[1,∞) c. [0,1]
51. Find the domain of the function d. [-1,1]
f(x)=√log 0.5 𝑥 59. Find the domain of the function
𝜋
a. (0,1) sin−1 𝑥 + cos −1 𝑥 = 2
b. [0,1] a. (-1,1)
c. {0,1} b. [-1,1]
d. None of these c. (0,1) d. [0,1]
In front of Tileshwarnath Mandir, Near SBI Chowk, Patna City (9386487790, 7903070219, 8248700030)
60. Find the domain of the function √9−𝑥 2
𝜋
68. Find the domain of the function sin−1 (3−𝑥)
sin−1 √𝑥 + cos−1 √𝑥 = 2
a. [2,3)
a. (-1,1)
b. [2,3]
b. [-1,1]
c. (2,3)
c. (0,1)
d. None of these
d. [0,1]
𝑥
69. Find the domain of the function
61. Find the domain of the function sin−1 log 2 2 tan−1 𝑥 − sin−1 𝑥 2
a. [1,4] a. R
b. (1,4) b. [-1,1]
c. [1,4) c. R-[-1,1]
d. (1,4] d. None of these
62. Find the domain of the function √sin−1 log 2 𝑥 1+𝑥 2
70. Find the domain of the function sin−1
2𝑥
a. (1,2)
a. (-1,1)
b. [1,2]
b. [-1,1]
c. (1,2]
c. {-1,1}
d. [1,2)
𝑥
d. None of these
63. Find the domain of the function sin−1 log 3 3 1+𝑥 2
71. Find the domain of the function sin−1
a. [1,9] 2𝑥
a. (-1,1)
b. (1,9)
b. [-1,1]
c. (1,9]
c. {-1,1}
d. [1,9)
𝑥2
d. R
64. Find the domain of the function sin−1 log 5 𝑥2
5 72. Find the domain of the function sin−1 log 2
a. (-5,-1) 2
a. R
b. [1,5]
b. [1,4]
c. [-5,-1]U[1,5]
c. R-(1,4)
d. None of these
d. None of these
65. Find the domain of the function
3 73. Find the domain of the function
log( 𝑥 3 − 𝑥) +4−𝑥 2 1
+ √𝑥 + 2
a. (-1,0) log10 ( 3−𝑥)

b. (-1,0)U(1,∞) a. [-2,3)
c. (-1,0)U(1,∞)-{2} b. [-3,2]
d. None of these c. [-2,3)-{2}
66. Find the domain of the function d. [-2,3]-{2}
1 74. Find the domain of the function
+ √𝑥 + 2
log10 ( 1−𝑥) tan−1 𝑥 + cos −1 𝑥 2
a. (-2,1) a. R-[-1,1]
b. [-2,1] b. R-(-1,1)
c. [-2,1)-{0} c. (-1,1)
d. None of these d. [-1,1]
sin−1 𝑥
67. Find the domain of the function 75. Find the domain of the function f()x=sin1/x
𝑥
a. [-1,1] a. R
b. R-(-1,1) b. R+
c. [-1,1]-{0} c. R0
d. None of these d. R-
In front of Tileshwarnath Mandir, Near SBI Chowk, Patna City (9386487790, 7903070219, 8248700030)
76. Find the domain of the function f(x)=sin−1 5𝑥 85. Find the range of the function f(x)=5-x2
a. (-1/5,1/5) a. R
b. [-1/5,1/5] b. (-∞,5)
c. R c. (-∞,5])
d. (0,1/5) d. None of these
77. Find the range of the function f(x)=1/x 86. Find the range of the function f(x)=x2/x2+1
a. R a. R
b. R0 b. R-(0,1)
c. R+ c. [0,1)
d. R- d. None of these
78. Find the range of the function f(x)=x+5/x-5 87. Find the range of the function
a. R f(x)=√4 − 16𝑥 2
b. R-{5} a. (0,2)
c. R-{1} b. [0,2]
d. None of these c. [1/4,∞)
79. Find the range of the function f(x)=1/x-2 d. None of these
a. R-{2} 88. Find the range of the function f(x)=x2-x-6/x-3
b. R-{0} a. R
c. R-{0,2} b. R-(3)
d. None of these c. (2,3)
80. Find the range of the function f(x)=x2+3 d. R-{5}
a. (3,∞) 89. Find the range of the function f(x)=x/1+x2
b. [3,∞) a. R
c. [3,∞] b. (-1/2,1/2)
d. None of these c. [-1/2,1/2]
81. Find the range of the function f(x)=1/x2+2 d. None of these
a. (0,1/2) 90. Find the range of the function f(x)=x2+3x+2
b. (0,1/2] a. (-1/4,∞)
c. R-{-2} b. [-1/4,∞)
d. R c. [-1/4,1/4]
82. Find the range of the function f(x)=√2𝑥 − 3 d. R
a. (0,∞) 91. Find the range of the function f(x)=x2-6x+7
b. [0,∞) a. (-2,∞)
c. R-{3/2} b. [-2,∞)
d. R+ c. (-2,2)
83. Find the range of the function f(x)=5-7x d. R
a. R 92. Find the range of the function f(x)=x2 - x+1
b. R-{5/7} a. R
c. R-{7/5} b. [-3/4,∞)
d. None of these c. [-3/4,3/4]
84. Find the range of the function f(x)=2-5x/3x-4 d. [3/4,∞)
a. R-{5/3} 𝑥 2 −𝑥+1
93. Find the range of the function f(x) = 𝑥 2+𝑥+1
b. R-{-5/3}
a. (1/3,∞)
c. R-{4/3}
b. (3,∞)
d. None of these
c. [1/3,3] d. (-∞,∞)
In front of Tileshwarnath Mandir, Near SBI Chowk, Patna City (9386487790, 7903070219, 8248700030)
 𝑥 2 +34𝑥−71 102. Find the range of the function
94. Find the range of the function f(x) = 𝑥 2 +2𝑥−7
f(x) = 3sinx+4cosx
a. R-(5,9)
a. [3,4]
b. (5,9)
b. [-5,5]
c. [3,2]
c. (-4,5)
d. None of these
d. None of these
95. Find the range of the function
103. Find the range of the function
f(x) = √𝑥 − 1 + √5 − 𝑥 f(x)=7cosx-24sinx
a. (√2,2) a. [-3,4]
b. (2,2√2) b. [-13,13]
c. [1,5] c. [-25,25]
d. None of these d. [-6,20]
96. Find the range of the function 104. Find the range of the function
2
f(x) = √𝑥 − 3𝑥 + 2 f(x)=5cosx-12sinx+7
a. [0,∞) a. [-3,4]
b. [1,2] b. [-13,13]
c. (0,∞) c. [-25,25]
d. [3,4) d. [-6,20]
97. Find the range of the function 105. Find the range of the function
2
f(x) = √𝑥 − 4𝑥 + 6 f(x)=5sinθ+3sin(θ+𝜋/3)+4
a. (-∞,∞) a. [-3,11]
b. (0,∞) b. [-3,4]
c. [0,∞) c. [-13,13]
d. None of these d. [-25,25]
98. Find the range of the function 106. Find the range of the function
f(x) = √3 − 2𝑥 − 𝑥 2 f(x)=5cosθ+3cos(θ+𝜋/3)+3
a. (0,2) a. [-3,11]
b. [0,2] b. [-3,4]
c. [-2,2] c. [-13,13]
d. [2,3] d. [-4,10]
𝑥 2 +𝑥+2 107. Find the range of the function f(x) =16-7sinx
99. Find the range of the function f(x) = 𝑥 2+𝑥+1
a. [5,12
a. R b. [10,25]
b. R-(1,2) c. [-13,13]
c. R-(1,7/3) d. [9,23]
d. (1,7/3] 108. Find the range of the function f(x) =1/2-sin3x
𝑥 2 −2𝑥+4
100. Find the range of the function f(x) = 𝑥 2−2𝑥+5 a. [1/3,1]
a. [3/4,1] b. [-1/3,1]
b. [3/4,0) c. [-1/3,1/3]
c. [3/4,1) d. None of these
d. None of these 109. Find the range of the function
2 4 2 4
101. Find the range of the function f(x) =sin x +cos x
a. [-1,1]
f(x)=log( 𝑥 2 − 𝑥 + 1)
b. [-5,5]
a. [√3/2, ∞) b. [log 3/4 , ∞)
c. {-1,1}
c. [3/4,∞) d. None of these
d. {1}
In front of Tileshwarnath Mandir, Near SBI Chowk, Patna City (9386487790, 7903070219, 8248700030)
110. Find the range of the function f(x) =1/+2sinx
a. [1/3,1]
b. [-1/3,1]
c. [-1/3,1/3]
d. None of these
111. Find the range of the function f(x) =1/2cosx-1
a. (-∞,-1/3]
b. [1,∞)
c. (-∞,-1/3]U[1,∞)
d. None of these
112. Find the range of the function
2
f(x)=sin x-sinx+1
a. [3/4,3]
b. [-1,1]
c. [0,1]
d. None of these
113. Find the Domain and range of the function
f(x)=9-xPx-5
a. [5,7]&{1,2,3}
b. [2,7]&{2,3,4}
c. [3,5]&{1,2,3}
d. None of these
114. Find the Domain and range of the function
f(x)=9-xCx-5
a. [5,7]&{1,2,3}
b. [3,5,7]&{1,2,3}
c. [3,4,5]&{1,3}
d. [3,4,5]&{1,2,3}

…………………The End………………………….

In front of Tileshwarnath Mandir, Near SBI Chowk, Patna City (9386487790, 7903070219, 8248700030)