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Byju's Answer
Standard XII
Mathematics
One - One function
If fx = sin...
Question
If
f
(
x
)
=
sin
(
[
x
]
π
)
x
2
+
x
+
1
, where [.] denotes the greatest integer function, then
A
f
is one-one
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B
f
is not one-one and non-constant
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C
f
is a constant function
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D
none of these
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Solution
The correct option is
C
f
is a constant function
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1
Similar questions
Q.
Assertion (A):
f
(
x
)
=
sin
{
[
x
]
π
}
1
+
x
2
is continuous on
R
(where
[
x
]
denotes greatest integer function of
x
).
Reason (R): Every constant function is continuous on
R
Q.
Let
f
(
x
)
=
[
x
]
+
1
{
x
}
+
1
,
f
o
r
f
:
[
0
,
5
2
)
→
(
1
2
,
3
]
where [x] denotes greatest integer function and {x} denotes fractional part function, then which of the following is/are true?
Q.
A function f(x) is defined by
f
(
x
)
=
[
x
2
]
−
1
x
2
−
1
for
x
2
≠
1
,
f
(
x
)
=
f
(
−
1
)
=
0
,where
[
x
]
denotes greatest integer function, then
Q.
If
f
(
x
)
=
[
x
]
|
x
|
,
x
≠
0
where [.] denotes the greatest integer function, then
f
′
(
1
)
is
Q.
Assertion :
f
:
R
→
R
defined by
f
(
x
)
=
7
x
−
[
7
x
]
where
[
⋅
]
denotes greatest integer less than equal to
x
and
x
∈
R
,
f
is not one-one function. Reason: Periodic functions are always many one.
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