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JEE Main Math Class 12 Continuity and Differentiability Part 2 Questions
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© examsnet.com
Question : 38
Total: 92
Let
f
,
g
:
R
→
R
be functions defined by
f
(
x
)
=
{
[
x
]
,
x
<
0
|
1
−
x
|
,
x
≥
0.
and
g
(
x
)
=
{
e
x
−
x
,
x
<
0
(
x
−
1
)
2
−
1
,
x
≥
0.
where
[
x
]
denote the greatest integer less than or equal to
x
. Then, the function fog is discontinuous at exactly :
[28-Jun-2022-Shift-2]
one point
two points
three points
four points
Validate
Solution:
f
(
x
)
=
{
[
x
]
,
x
<
0
|
1
−
x
|
,
x
≥
0
and
g
(
x
)
=
{
e
x
−
x
,
x
<
0
(
x
−
1
)
2
−
1
,
x
≥
0
f
∘
g
(
x
)
=
{
[
g
(
x
)
]
,
g
(
x
)
<
0
|
1
−
g
(
x
)
|
,
g
(
x
)
≥
0
.
=
{
|
1
+
x
−
e
x
|
,
x
<
0
1
,
x
=
0
[
(
x
−
1
)
2
−
1
]
,
0
<
x
<
2
|
2
−
(
x
−
1
)
2
|
,
x
≥
2
So,
x
=
0
,
2
are the two points where fog is discontinuous.
© examsnet.com
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