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Byju's Answer
Standard XIII
Mathematics
Fractional Part Function
The domain of...
Question
The domain of the function
f
(
x
)
=
1
[
x
]
2
−
7
[
x
]
+
10
is
(where
[
.
]
denotes the greatest integer function)
A
R
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B
R
−
[
5
,
6
)
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C
R
−
[
2
,
3
)
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D
R
−
[
2
,
3
)
∪
[
5
,
6
)
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Solution
The correct option is
D
R
−
[
2
,
3
)
∪
[
5
,
6
)
f
(
x
)
=
1
[
x
]
2
−
7
[
x
]
+
10
For function to be defined,
[
x
]
2
−
7
[
x
]
+
10
≠
0
⇒
(
[
x
]
−
5
)
(
[
x
]
−
2
)
≠
0
⇒
[
x
]
≠
2
,
5
⇒
x
∉
[
2
,
3
)
and
x
∉
[
5
,
6
)
∴
Domain of
f
(
x
)
=
R
−
[
2
,
3
)
∪
[
5
,
6
)
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2
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