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JEE Main Math Class 11 Relations and Functions Part 2 Questions
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© examsnet.com
Question : 20
Total: 95
Let the range of the function
f
(
x
)
=
1
2
+
s
i
n
3
x
+
cos
3
x
,
x
∈
IR
be
[
a
,
b
]
.
If
α
and
β
are respectively the A.M. and the G.M. of
a
and
b
, then
α
β
is equal to :
[9 Apr 2024 Shift 2]
√
2
2
√
π
π
Validate
Solution:
👈: Video Solution
f
(
x
)
1
2
+
s
i
n
3
x
+
cos
3
x
[
1
2
+
√
2
,
1
2
−
√
2
]
α
β
=
a
+
b
2
√
a
b
=
1
2
(
√
a
b
+
√
b
a
)
=
1
2
(
√
2
−
√
2
2
+
√
2
+
√
2
+
√
2
2
−
√
2
)
=
(
2
−
√
2
)
+
(
2
+
√
2
)
2
×
√
2
=
√
2
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