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Byju's Answer
Standard XII
Mathematics
Continuity of a Function
Given fx = ...
Question
Given
f
(
x
)
=
x
2
+
a
, if
x
≤
0
=
2
√
1
+
x
2
+
b
, if
x
>
0
and
f
(
−
1
)
=
2
, if
f
is continuous at
x
=
0
, then
(
a
,
b
)
≡
____
A
(
−
1
,
1
)
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B
(
0
,
1
)
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C
(
1
,
0
)
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D
(
1
,
−
1
)
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Solution
The correct option is
B
(
1
,
−
1
)
Given
f
(
−
1
)
=
2
then from the definition of
f
(
x
)
we have,
1
+
a
=
2
or,
a
=
1
.
Since the function is continuous at
x
=
0
then,
lim
x
→
0
−
f
(
x
)
=
lim
x
→
0
+
f
(
x
)
or,
a
=
2
+
b
or,
1
=
2
+
b
[ Using the value of
a
]
or,
b
=
−
1
.
Then
(
a
,
b
)
=
(
1
,
−
1
)
.
Suggest Corrections
0
Similar questions
Q.
If
f
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1
-
1
-
x
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,
then
f
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(b) continuous on [−1, 1] and differentiable on
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∪
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(c) continuous and differentiable on [−1, 1]
(d) none of these
Q.
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⎪ ⎪ ⎪ ⎪ ⎪ ⎪
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Assertion :If
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g
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x
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⎨
⎩
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∪
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{
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1
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∞
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−
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o
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Q.
If
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=
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, where
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(
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−
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k
x
x
2
:
x
≠
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=
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2
:
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Q.
f
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⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
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x
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,
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>
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b
x
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sin
x
2
x
x
<
0
find
a
+
b
if
f
(
x
)
is continuous at
x
=
0
.
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