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Byju's Answer
[[x]]=[x] ∀ x...
Question
[
[
x
]
]
=
[
x
]
∀
x
∈
R
,
Where
[
.
]
denotes the greatest integer function.
A
True
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B
False
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Solution
The correct option is
A
True
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Similar questions
Q.
[
x
2
]
+
[
x
+
1
2
]
=
[
x
]
∀
x
∈
R
,
where
[
.
]
denotes the greatest integer function.
Q.
Prove that the Greatest integer function
f
:
R
→
R
given by
f
(
x
)
=
[
x
]
, is neither one-one nor onto, where
[
x
]
denotes the greatest integer less than or equal to
x
.
Q.
Determine the continuity of the function
f
(
x
)
=
[
x
2
]
−
[
x
]
2
,
∀
x
∈
R
at the end point of the interval
[
−
1
,
0
]
. Where
[
.
]
denotes the greatest integer function.
Q.
If
[
x
]
denotes greatest integer function of
x
, then the domain
[
x
]
is
R
, while the range is
I
Q.
If
f
:
R
→
R
is a function defined by
f
(
x
)
=
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x
−
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]
cos
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2
)
π
, where [.] denotes the greatest integer function, then
f
is:
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