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Byju's Answer
Standard XII
Mathematics
Definition of Functions
Which of the ...
Question
Which of the following relations are functions from A = { 1, 4, 9, 16 } to B = { -1, 2, -3, -4, 5, 6 }. In case of a function, write down its range.
f
2
= { (1, -4), (1, -1), (9, -3), (16, 2) }.
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Solution
Since element
1
in set
A
have two images in
B
therfore
f
2
is not a function.
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Similar questions
Q.
Which of the following relations are functions from A = { 1, 4, 9, 16 } to B = { -1, 2, -3, -4, 5, 6 }. In case of a function, write down its range.
f
1
= { (1, -1), (4, 2), (9, -3), (16, -4) }
Q.
Let
A
=
{
1
,
2
,
3
,
4
}
,
B
=
{
1
,
5
,
9
,
11
,
15
,
16
}
and
f
=
{
(
1
,
5
)
,
(
2
,
9
)
,
(
3
,
1
)
,
(
4
,
5
)
,
(
2
,
11
)
}
Are the following true?
(i)
f
is a relation from
A
to
B
(ii)
f
is a function from
A
to
B
Justify your answer in each case
Q.
Which of the following relations are functions? Give reasons.
If it is a function determine its domain and range
(i)
{
(
2
,
1
)
,
(
5
,
1
)
,
(
8
,
1
)
,
(
11
,
1
)
,
(
14
,
1
)
,
(
17
,
1
)
}
(ii)
{
(
2
,
1
)
,
(
4
,
2
)
,
(
6
,
3
)
,
(
8
,
4
)
,
(
10
,
5
)
,
(
12
,
6
)
,
(
14
,
7
)
}
(iii)
{
(
1
,
3
)
,
(
1
,
5
)
,
(
2
,
5
)
}
Q.
If X= { 1, 2, 3, 4, 5 }, Y= { 1, 3, 5, 7, 9 } determine which of the following relations from X to Y are functions? Give reason for your answer. If it is a function, state its type.
(i)
R
1
={(x, y)| y=x+2, x
ϵ
X, y
ϵ
Y}
(ii)
R
2
= { (1, 1), (2, 1), (3, 3), (4, 3), (5, 5) }
(iii)
R
3
= { (1, 1), (1, 3), (3, 5), (3, 7), (5, 7) }
(iv)
R
4
= { (1, 3), (2, 5), (4, 7), (5, 9), (3, 1) }
Q.
For the given function F= { (1, 3), (2, 5), (4, 7), (5, 9), (3, 1) }, write the domain and range.
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