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JEE Main Math Class 11 Relations and Functions Part 2 Questions
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© examsnet.com
Question : 8
Total: 95
Consider the function
f
:
ℝ
⟶
ℝ
defined by
f
(
x
)
=
2
x
√
1
+
9
x
2
. If the composition of
f
,
⏟
(
f
∘
f
o
o
o
o
10times
)
(
x
)
=
2
10
x
√
1
+
9
α
x
2
, then the value of
√
3
α
+
1
is equal to .........
[4 Apr 2024 Shift 2]
Your Answer:
Validate
Solution:
👈: Video Solution
f
(
f
(
x
)
)
=
2
f
(
x
)
√
1
+
9
f
2
(
x
)
=
4
x
√
1
+
9
x
2
+
9.2
2
x
2
f
(
f
(
f
(
x
)
)
)
=
2
3
x
∕
√
1
+
9
x
2
√
1
+
9
(
1
+
2
2
)
2
2
x
2
1
+
9
x
2
=
2
3
x
√
1
+
9
x
2
(
1
+
2
2
+
2
4
)
∴
By observation
α
=
1
+
2
2
+
2
4
+
.
.
.
.
+
2
18
=
1
(
(
2
2
)
10
−
1
2
2
−
1
)
=
2
20
−
1
3
3
α
+
1
=
2
20
⟶
√
3
α
+
1
=
2
10
=
1024
© examsnet.com
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