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JEE Main Math Class 11 Relations and Functions Part 2 Questions
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© examsnet.com
Question : 55
Total: 95
If the domain of the function
f
(
x
)
=
log
e
(
4
x
2
+
11
x
+
6
)
+
s
i
n
−
1
(
4
x
+
3
)
+
cos
−
1
(
10
x
+
6
3
)
is
(
α
,
β
]
, then
36
|
α
+
β
|
is equal to
[15-Apr-2023 shift 1]
72
63
45
54
Validate
Solution:
f
(
x
)
=
ln
(
4
x
2
+
11
x
+
6
)
+
s
i
n
−
1
(
4
x
+
3
)
+
cos
−
1
(
10
x
+
6
3
)
(i)
4
x
2
+
11
x
+
6
>
0
4
x
2
+
8
x
+
3
x
+
6
>
0
(
4
x
+
3
)
(
x
+
2
)
>
0
x
∈
(
−
∞
,
−
2
)
∪
(
−
3
4
,
∞
)
(ii)
4
x
+
3
∈
[
−
1
,
1
]
x
∈
[
−
1
,
−
1
∕
2
]
(iii)
10
x
+
6
3
∈
[
−
1
,
1
]
x
∈
[
−
9
10
,
−
3
10
]
x
∈
(
−
3
4
,
−
1
2
]
α
=
−
3
4
,
β
=
−
1
2
α
+
β
=
−
5
4
36
|
α
+
β
|
=
45
© examsnet.com
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