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Byju's Answer
Standard XII
Mathematics
Monotonically Increasing Functions
Function fx...
Question
Function
f
(
x
)
=
[
x
]
is discontinuous at-
A
Every real number
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B
Every natural number
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C
Every integer
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D
No where
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Solution
The correct option is
C
Every integer
from the graph of
[
x
]
we can see that
[
x
]
is discontinuous at every integer
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0
Similar questions
Q.
A function is given by
f
(
x
)
=
log
x
.
e
x
. Then
f
(
x
)
is
Q.
The function
f
(
x
)
=
e
x
.
l
o
g
x
is discontinuous at
in the domain.
Q.
If
f
(
x
)
is a real valued function discontinuous at all integral points lying in
[
0
,
n
]
and if
(
f
(
x
)
)
2
=
1
∀
x
∈
[
0
,
n
]
,
then number of functions
f
(
x
)
are
Q.
Assertion :Let
f
(
x
)
=
⎧
⎨
⎩
1
+
x
x
<
0
1
+
[
x
]
+
sin
x
0
≤
x
≤
π
/
2
3
x
≥
π
/
2
f is continuous on R
−
{
1
}
Reason: The greatest integer function is discontinuous at every integer.
Q.
Consider the functions
f
(
x
)
=
s
i
n
(
x
−
1
)
and
g
(
x
)
=
cot
−
1
[
x
−
1
]
Assertion: The function
F
(
x
)
=
f
(
x
)
.
g
(
x
)
is discontinuous at
x
=
1
Reason: If
f
(
x
)
is discontinuous at
x
=
a
and
g
(
x
)
is also discontinuous at
x
=
a
then the product function
f
(
x
)
.
g
(
x
)
is discontinuous at
x
=
a
.
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