242
Question
Let
f
be the subset of Z
× Z
defined by f
=
{(ab,
a
+ b):
a,
b
∈
Z}.
Is f
a function from Z
to Z:
justify your answer.
Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.
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Solution
The
relation f
is defined as f
=
{(ab,
a
+ b):
a,
b
∈
Z}
We
know that a relation f
from a set A to a set B is said to be a function if every element of
set A has unique images in set B.
Since
2, 6, –2, –6 ∈
Z,
(2 × 6, 2 + 6), (–2 × –6, –2 + (–6))
∈
f
i.e.,
(12, 8), (12, –8) ∈
f
It
can be seen that the same first element i.e., 12 corresponds to two
different images i.e., 8 and –8. Thus, relation f
is not a function.
The relation f is defined as f = {(ab, a + b): a, b ∈ Z}
We know that a relation f from a set A to a set B is said to be a function if every element of set A has unique images in set B.
Since 2, 6, –2, –6 ∈ Z, (2 × 6, 2 + 6), (–2 × –6, –2 + (–6)) ∈ f
i.e., (12, 8), (12, –8) ∈ f
It can be seen that the same first element i.e., 12 corresponds to two different images i.e., 8 and –8. Thus, relation f is not a function.
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