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Relations and Functions
- Online Test
Relations and Functions
TEST : 8
Relations and Functions
Prepare / Learn
Q1.
The range of the function
f
(
x
)
=
x
2
−
x
+
1
x
2
+
x
+
1
is
A.
[3, ∞∞)
B.
[1/3,3]
C.
none of these
D.
R
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
No Explaination.
Relations and Functions
Prepare / Learn
Q2.
On the set Z of all integers define f ; Z
→
Z as follows : f ( x ) = x/2 if x is even , and f ( x ) = 0 if x is odd , then f is
A.
one-one but not onto
B.
into
C.
one-one and onto
D.
onto but not one-one
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
No Explaination.
Relations and Functions
Prepare / Learn
Q3.
Let f : R
→
R be defined by f (x) = 3x – 4, then
f
−
1
(x) is equal to
A.
none of these.
B.
x+4/3
C.
3x+4
D.
x/3-4
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
No Explaination.
Relations and Functions
Prepare / Learn
Q4.
In the set W of whole numbers an equivalence relation R defined as follow : aRb iff both a and b leave same remainder when divided by 5. The equivalence class of 1 is given by
A.
{2, 7, 12, 17…}
B.
[0, 5, 10, 15,…}
C.
{1, 6, 11, 16, ….}
D.
{4, 9, 14, 19, …}.
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
No Explaination.
Relations and Functions
Prepare / Learn
Q5.
If f (x)
=
x
−
1
x
+
1
,
,
then
(
f
1
f
(
x
)
)
equals
A.
1
B.
0
C.
x
D.
1/x
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
No Explaination.
Relations and Functions
Prepare / Learn
Q6.
If
A
=
{
(
x
,
y
)
:
x
2
+
y
2
=
25
}
and
B
=
{
(
x
,
y
)
:
x
2
+
9
y
2
+
y
2
=
144
}
,
then
A
∩
B
A
∩
B
contains
A.
one point
B.
four points
C.
two points
D.
one point
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
No Explaination.
Relations and Functions
Prepare / Learn
Q7.
If f(x) =
x
x
−
1
=
1
y
,
,
then f (y) =
A.
1+x
B.
1-x
C.
x
D.
x-1
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
No Explaination.
Relations and Functions
Prepare / Learn
Q8.
The function f (x) = log
(
1
+
x
1
−
x
)
satisfies the equation
A.
f
(
x
1
)
+
f
(
x
2
)
=
f
(
x
1
+
x
2
)
B.
f
(
x
)
+
f
(
x
+
1
)
=
f
(
x
2
+
x
)
C.
f
(
x
1
)
+
f
(
x
2
)
=
f
(
x
1
+
x
2
)
D.
f
(
x
1
)
+
f
(
x
2
)
=
f(
x
1
+
x
2
/1+
x
1
x
2
)
x
2
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
No Explaination.
Relations and Functions
Prepare / Learn
Q9.
If f (x + y + z) = f (x) f (y ) f (z) for all x , y z and if f (2) = 4, f’ (0) = 5 and f (0)
≠
≠
0, then f’ (2) is equal to
A.
±20
B.
±100
C.
±30
D.
±80
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
No Explaination.
Relations and Functions
Prepare / Learn
Q10.
The domain of the function
1
[
x
]
+
2
x
−
x
2
−
−
−
−
−
−
√
is
A.
[0,1)
B.
[0,2]
C.
[1,2)
D.
[1,2]
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
No Explaination.
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Relations and Functions
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