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Byju's Answer
Standard XII
Mathematics
Bijective Function
If N→ N is d...
Question
If
N
→
N
is defined by
f
(
n
)
=
n
−
(
−
1
)
n
, then
A
f is one-one but not onto
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B
f is both one-one and onto
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C
f is neither one-one nor onto
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D
f is onto but not one-one
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Solution
The correct option is
B
f is both one-one and onto
This function f maps
1
→
2
,
2
→
1
3
→
4
,
4
→
3
5
→
6
,
6
→
5
i.e.,
2
m
−
1
→
2
m
and
2
m
→
2
m
−
1
So f is one-one and onto.
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