1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Many-One onto Function
Let f:N× N→...
Question
Let
f
:
N
×
N
→
N
−
{
1
}
be defined as
f
(
m
,
n
)
=
m
+
n
, then function
f
is ______.
A
One-One and onto
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Many- One and not onto
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
One- One and not onto
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Many- One and onto
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
D
One-One and onto
Given
f
(
m
,
n
)
=
m
+
n
Range of this function is set of all natural numbers except
1
[since least value of
m
and
n
is
1
]
Therefore the range and co-domain are equal
Therefore it is onto
For every
(
m
,
n
)
, there exists only one
m
+
n
Therefore it is one-one also
Hence,
f
is one-one and onto.
Suggest Corrections
0
Similar questions
Q.
Let
N
be the set of natural numbers and two functions
f
and
g
be defined as
f
,
g
:
N
→
N
such that
f
(
n
)
=
⎧
⎪ ⎪
⎨
⎪ ⎪
⎩
n
+
1
2
if
n
is odd
n
2
if
n
is even
and
g
(
n
)
=
n
−
(
−
1
)
n
. Then
f
∘
g
is :
Q.
Let
f
:
R
-
n
→
R
be a function defined by
f
x
=
x
-
m
x
-
n
,
where
m
≠
n
.
Then,
(a) f is one-one onto
(b) f is one-one into
(c) f is many one onto
(d) f is many one into
Q.
If
N
→
N
is defined by
f
(
n
)
=
n
−
(
−
1
)
n
, then
Q.
Let
A
=
{
0
,
1
}
and
N
the set of all natural numbers. Then show that the mapping
f
:
N
→
A
defined by
f
(
2
n
−
1
)
=
0
,
f
(
2
n
)
=
1
∀
n
∈
N
is many-one onto.
Q.
If a function
f
is defined as
f
:
Z
→
Z
,
f
(
n
)
=
{
n
2
:
n
is even
−
n
+
1
2
:
n
is odd
then prove that
f
is onto but not one-one.
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
MATHEMATICS
Watch in App
Explore more
Many-One onto 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