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Byju's Answer
Standard XI
Mathematics
Domain
The domain of...
Question
The domain of
cos
−
1
[
2
x
2
−
3
]
,
where
[
.
]
denotes the greatest integer function, is
A
(
−
√
5
2
,
−
√
1
2
)
∪
(
√
1
2
,
√
5
2
)
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B
[
−
√
5
2
,
−
1
]
∪
[
1
,
√
5
2
]
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C
(
−
√
5
2
,
−
1
]
∪
[
1
,
√
5
2
)
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D
[
−
√
2
,
−
1
]
∪
[
1
,
√
2
]
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Solution
The correct option is
C
(
−
√
5
2
,
−
1
]
∪
[
1
,
√
5
2
)
For
cos
−
1
to be defined,
−
1
≤
[
2
x
2
−
3
]
≤
1
⇒
−
1
≤
2
x
2
−
3
<
2
⇒
1
≤
x
2
<
5
2
⇒
x
∈
(
−
√
5
2
,
−
1
]
∪
[
1
,
√
5
2
)
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