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Byju's Answer
Standard XII
Mathematics
Definition of Functions
The equation ...
Question
The equation
|
|
x
−
1
|
+
a
|
=
4
can have real solution for
x
if
a
belongs to the interval
A
(
−
∞
,
4
]
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B
(
−
∞
,
−
4
]
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C
[
4
,
+
∞
)
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D
[
−
4
,
4
]
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Solution
The correct option is
A
(
−
∞
,
4
]
1) When
x
=
1
,
|
a
|
=
4
a
=
±
4
2) When
x
>
1
|
x
−
1
+
a
|
=
4
x
−
1
+
a
=
4
x
=
5
−
a
5
−
a
>
1
a
<
4
3) When
x
<
1
,
−
x
+
1
−
a
=
4
x
=
−
a
−
3
−
a
−
3
>
1
a
<
−
4
Hence, option A is correct.
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