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JEE Main Math Class 12 Continuity and Differentiability Part 1 Questions
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© examsnet.com
Question : 58
Total: 100
Let f be a composite function of x defined by
f
(
u
)
=
1
u
2
+
u
−
2
,
u
(
x
)
=
1
x
−
1
.
Then the number of points x where f is discontinuous is :
[Online April 23, 2013]
4
3
2
1
Validate
Solution:
µ
(
x
)
=
1
x
−
1
,
which is discontinous at
x
=
1
f
(
u
)
=
1
u
2
+
u
−
2
=
1
(
u
+
2
)
(
u
−
1
)
which is discontinous at
u
=
−
2
,
1
when
u
=
−
2
,
then
1
x
−
1
=
−
2
⇒
x
=
1
2
when
u
=
1
,
then
1
x
−
1
=
1
⇒
x
=
2
Hence given composite function is discontinous at three points,
x
=
1
,
1
2
and 2 .
© examsnet.com
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