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Test Index
JEE Main Math Class 11 Relations and Functions Part 1 Questions
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Question : 28
Total: 100
The real valued function
f
(
x
)
=
c
o
s
e
c
−
1
x
√
x
−
[
x
]
, where
[
x
]
denotes the greatest integer less than or equal to
x
, is defined for all
x
belonging to
[2021, 18 March Shift-I]
all reals except integers
all non-integers except the interval [
−
1
,
1
]
all integers except 0,
−
1
,
1
all reals except the interval
[
−
1
,
1
]
Validate
Solution:
Given,
f
(
x
)
=
c
o
s
e
c
−
1
x
√
x
−
[
x
]
⇒
f
(
x
)
=
c
o
s
e
c
−
1
x
√
{
x
}
For
f
(
x
)
to be defined,
{
|
x
|
≥
1
{
x
}
>
0.
⇒
{
x
≤
−
1
or
x
≥
1
x
≠
1
integers
.
i.e.
x
∈
(
−
∞
,
−
1
]
∪
[
1
,
∞
)
−
{
integers
}
i.e. all non-integers except the interval
[
−
1
,
1
]
(here,
−
1
and 1 are included in except case, because of
−
1
and 1 are integers).
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