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Byju's Answer
Standard XII
Mathematics
Geometrical Explanation of Intermediate Value Theorem
The function ...
Question
The function
f
(
x
)
=
4
−
x
2
4
x
−
x
3
is
A
discontinuous at only one point
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B
discontinuous exactly at two points
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C
discontinuous exactly at three points
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D
None of these
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Solution
The correct option is
C
discontinuous exactly at three points
Denominator is having
3
roots
x
=
0
,
2
and
−
2.
So, discontinuous at
3
points.
Hence, 'C' is the answer.
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Similar questions
Q.
The function
f
x
=
4
-
x
2
4
x
-
x
3
(a) discontinuous at only one point
(b) discontinuous exactly at two points
(c) discontinuous exactly at three points
(d) none of these
Q.
The function
f
(
x
)
=
|
x
2
−
2
x
−
3
|
⋅
e
|
9
x
2
−
12
x
+
4
|
is not differentiable at exactly :
Q.
Consider the two curves
C
1
:
y
2
=
4
x
,
C
2
:
x
2
+
y
2
−
6
x
+
1
=
0.
Then,
Q.
Let
f
:
[
−
1
2
,
2
]
→
R
and
g
:
[
−
1
2
,
2
]
→
R
be functions defined by
f
(
x
)
=
[
x
2
−
3
]
and
g
(
x
)
=
|
x
|
f
(
x
)
+
|
4
x
−
7
|
f
(
x
)
,
where
[
y
]
denotes the greatest integer less than or equal to
y
for
y
∈
R
.
Then
Q.
If f(x) = sgn (x) and
g
(
x
)
=
x
(
1
−
x
2
)
then (fog)(x) is
discontinuous at
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