9
You visited us
9
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Bijective Function
Which of the ...
Question
Which of the following functions are bijective?
A
f
:
R
→
[
0
,
∞
)
defined as
f
(
x
)
=
e
sgn
(
x
)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
f
:
[
3
,
4
]
→
[
4
,
6
]
defined by
f
(
x
)
=
|
x
−
1
|
+
|
x
−
2
|
+
|
x
+
3
|
+
|
x
−
4
|
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
f
:
R
→
R
defined by
f
(
x
)
=
[
x
]
+
cos
(
π
[
x
]
)
where
[
.
]
denotes the greatest integer function
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
f
:
R
→
R
defined as
f
(
x
)
=
min
{
x
+
2
,
−
2
x
+
4
}
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
B
f
:
[
3
,
4
]
→
[
4
,
6
]
defined by
f
(
x
)
=
|
x
−
1
|
+
|
x
−
2
|
+
|
x
+
3
|
+
|
x
−
4
|
sgn
(
x
)
=
⎧
⎪
⎨
⎪
⎩
|
x
|
x
,
x
≠
0
0
,
x
=
0
sgn
(
x
)
=
⎧
⎨
⎩
−
1
,
x
<
0
0
,
x
=
0
1
,
x
>
0
∴
e
sgn
(
x
)
=
⎧
⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪
⎩
e
−
1
=
1
e
,
x
<
0
e
0
=
1
,
x
=
0
e
1
=
e
,
x
>
0
Neither one-one nor onto.
Hence,
e
sgn
(
x
)
is not bijective.
f
:
[
3
,
4
]
→
[
4
,
6
]
f
(
x
)
=
|
x
−
1
|
+
|
x
+
2
|
+
|
x
−
3
|
+
|
x
−
4
|
For
3
≤
x
≤
4
f
(
x
)
=
x
−
1
+
x
−
2
+
x
−
3
+
4
−
x
=
2
x
−
2
f
is one-one.
3
≤
x
≤
4
⇒
6
≤
2
x
≤
8
⇒
4
≤
2
x
−
2
≤
6
f
is onto.
It is bijective.
f
:
R
→
R
f
(
x
)
=
[
x
]
+
cos
π
[
x
]
If
0
≤
x
<
1
,
f
(
x
)
=
0
+
cos
π
(
0
)
=
1
Not one-one, so, not bijective.
f
:
R
→
R
f
(
x
)
=
min
{
x
+
2
,
−
2
x
+
4
}
Not one-one
Not onto.
So,
f
is not bijective.
Suggest Corrections
0
Similar questions
Q.
Which of the following functions are bijections?
Q.
In the following functions defined from
[
−
1
,
1
]
to
[
−
1
,
1
]
, then functions which are not bijective are
Q.
Which of the following functions from
Z
to itself are bijections?
Q.
If the following functions have both domain and co-domain as
[
−
1
,
1
]
, then select those which are not bijective?
Q.
If the following functions have both domain and co-domain as
[
−
1
,
1
]
, then select those which are not bijective?
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Types of Functions
MATHEMATICS
Watch in App
Explore more
Bijective Function
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app