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Byju's Answer
Standard XII
Mathematics
Greatest Integer Function
The graphs of...
Question
The graphs of the polynomial
x
2
−
1
and
cos
x
intersect
A
at exactly two points
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B
at exactly
3
points
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C
at least
4
but at finitely many points
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D
at infinitely many points
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Solution
The correct option is
A
at exactly two points
The graph of
y
=
x
2
−
1
and
y
=
cos
x
as shown below
They intersect at exactly two points.
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2
Similar questions
Q.
Let
f
(
x
)
=
tan
(
π
[
x
−
π
]
)
1
+
[
x
]
2
, where
[
.
]
denotes the greatest integer function. Then
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 equation
e
x
−
x
−
1
=
0
has
Q.
Consider the two curves
C
1
:
y
2
=
4
x
,
C
2
:
x
2
+
y
2
−
6
x
+
1
=
0.
Then,
Q.
If
f
(
x
)
=
⎧
⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪
⎩
x
2
+
2
,
x
<
0
−
2
e
−
x
,
0
≤
x
<
2
,
−
2
e
2
(
x
−
3
)
,
x
≥
2
then
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