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Tardigrade
Question
Mathematics
Function f: N → N, f (x)=2x+3 is
Q. Function
f
:
N
→
N
,
f
(
x
)
=
2
x
+
3
is
2634
181
UPSEE
UPSEE 2016
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A
One-one Onto function
B
One-one Into function
C
Many- one Onto function
D
Many -one Into function
Solution:
Let
x
1
and
x
2
be any two elements of
N
.
∴
f
(
x
1
)
=
f
(
x
2
)
⇒
2
x
1
+
3
=
2
x
2
+
3
⇒
x
1
=
x
2
∴
f
is one-one function.
Now, let
y
=
2
x
+
3
⇒
x
=
2
y
−
3
It is not onto function, because for
y
=
3
,
x
=
0
∈
/
N
.
Hence, it is one-one into function.