FUNCTION (Domain of Function)
1.
The largest set of real values of x for which f(x)  (x  2)(5  x) 
(a) [1, 2]  (2,5)
(c) [3,4]
2.
MITTAL CLASSES
Page |1
1
x 4
2
is a real function
(b) (2,5]
(d) None of these
The domain of the function f(x) 
1
 x  2 is
log10 (1  x)
(a) (3,  2.5 )  (2.5,  2)
(c) (0,1)
(b) ( 2,0 )  (0, 1)
(d) None of these
3.
The domain of the function f(x)  loge (x  [x]), where [.] denotes the greatest integer function, is
(a) R
(b) R–Z
(c) (0,  )
(d) None of these
4.
The domain of the function f(x) 
5.
6.
7.
sin1(3  x)
is
ln(| x | 2)
(a) [ 2,4]
(b) (2, 3)  (3, 4]
(c) [2,  )
(d) ,  3 )  [2, )
Domain of the function f(x)  sin1(1  3x  2x 2 ) is
(a) ( , )
(b) ( 1,1)
 3 
(c)  ,0 
2 
1

(d)  ,   (2, )
2

 4  x2
Domain of the function sinln 
 1 x

(a) [ 2,1]
(c) [2,1)




(b) (2,1)
(d) ( 2,1]
Domain of the function f(x)  log0.5 (3x  8)  log0.5 (x2  4) is
8 
(a)  ,  
3 
(c) ( , )
8.
9.
8

(b)  , 
3

(d) (0,  )
The domain of f(x) 
1
| cos x |  cos x
is
(a) [2n,2n]
(b) (2n, 2n  1)
 (4n  1)  (4n  3) 
(c) 
,

2
2


 (4n  1 4n  1) 
(d) 
,

2
2


 1  x2 
2
The domain of f(x)  sin1 
  1  x is
2x


(a) {1}
(c) {1,–1}
(b) ( 1,1)
(d) None of these
Mittal Classes, Near Axis Bank, Rasulpur Chowk, Palwal, Haryana-121102
Mob: 7027886056 Email: mittalclassespwl@gmail.com
FUNCTION (Domain of Function)
10.
MITTAL CLASSES
Page |2
 1 
The domain of the function f(x)  log 
 is
 | sin x | 
(a) R  {, }
(b) R  {n | n  Z}
(c) R  {2n | n  Z}
(d) ( , )
11.
The domain of the function f(x)  16  x C2x 1  20 3xP4x 5 , where the symbols have
meanings, is the set
(a) {2, 3}
(b) {2, 3, 4}
(c) {1, 2, 3, 4}
(d) {1, 2, 3, 4, 5}
12.
Domain of the function f(x)  sin1 {1  e x )1 is
(a) (– , )
(b) [1,0]
(d) [–1, 1]
(c) [0,1]
13.
If n is an integer then domain of the function

(a) [n  ,n]
2
(c) [(2n  1),2n]
15.
Domain of definition of the function f(x) 
(a) (1, 2)
(c) (1, 2)  (2,  )
16.
sin2x is


(b) n,n  
2

(d) [2n,(2n  1)]
3
 log10 (x 3  x), is
2
4x
(b) (–1, 0)  (1, 2)
(d) (–1, 0)  (1, 2)  (2,  )
The domain of the function f(x)  log3  x (x 2  1) is
(a) (3,  1)  (1, )
(c) (3, 2)  (2,  1)  (1, )
17.
their usual
(b) [3,  1)  [1, )
(d) [3,  2)  (2,  1)  [1, ]

, for real value x, is
6
 1 1
(b)   , 
 2 2
 1 1
(d)   , 
 4 4
Domain of definition of the function f(x)  sin1(2x) 
 1 1
(a)   , 
 4 2
 1 1
(c)   , 
 2 9
Answer key
1.
2.
3.
4.
B
B
B
B
5.
6.
7.
8.
C
B
A
D
9.
10.
11.
12.
C
B
A
A
Mittal Classes, Near Axis Bank, Rasulpur Chowk, Palwal, Haryana-121102
Mob: 7027886056 Email: mittalclassespwl@gmail.com
13.
15.
16.
17.
B
D
C
A