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Byju's Answer
Standard XI
Mathematics
Range
The number of...
Question
The number of integer(s) in the range of
√
[
sgn
(
x
)
]
2
−
{
sgn
(
x
)
}
2
is
(where
[
.
]
,
{
.
}
and
sgn
(
x
)
represent the greatest integer function, fractional part function and signum function respectively)
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Solution
y
=
√
[
sgn
(
x
)
]
2
−
{
sgn
(
x
)
}
2
sgn
(
x
)
=
⎧
⎨
⎩
−
1
,
x
<
0
0
,
x
=
0
1
,
x
>
0
⇒
[
sgn
(
x
)
]
=
⎧
⎨
⎩
−
1
,
x
<
0
0
,
x
=
0
1
,
x
>
0
⇒
[
sgn
(
x
)
]
2
=
{
1
,
x
≠
0
0
,
x
=
0
{
sgn
(
x
)
}
=
0
∀
x
∈
R
∴
y
=
√
[
sgn
(
x
)
]
2
⇒
y
=
0
,
1
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0
Similar questions
Q.
The number of integer(s) in the range of
√
[
sgn
(
x
)
]
2
−
{
sgn
(
x
)
}
2
is
(where
[
.
]
,
{
.
}
and
sgn
(
x
)
represent the greatest integer function, fractional part function and signum function respectively)
Q.
The number of integer(s) in the range of
√
[
sgn
(
x
)
]
2
−
{
sgn
(
x
)
}
2
is
(Here,
[
.
]
,
{
.
}
and
sgn
(
x
)
represent the greatest integer function, fractional part function and signum function respectively)
Q.
Let
f
:
A
→
R
+
be a function defined by
f
(
x
)
=
log
{
x
}
(
x
−
[
x
]
|
x
|
)
, where
[
.
]
and
{
.
}
represent greatest integer function and fractional part function respectively. If
B
is the range of
f
, then the number of integer(s) in
R
+
−
B
is
Q.
Let
f
:
A
→
R
be a function defined by
f
(
x
)
=
log
{
x
}
(
x
−
[
x
]
|
x
|
)
, where
[
.
]
and
{
.
}
represent greatest integer function and fractional part function respectively. If
B
is the range of
f
, then the number of integer(s) in
R
−
B
is
Q.
∫
4
1
{
x
}
[
x
]
d
x
is equal to (where
[
.
]
and
{
.
}
represent greatest integer function and fractional part function respectively.).
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