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KoMaL A Problems 2023/2024
A. 861
Iteration of x^2-2
Iteration of x^2-2
Source: KoMaL A861
November 11, 2023
algebra
komal
Problem Statement
Let
f
(
x
)
=
x
2
−
2
f(x)=x^2-2
f
(
x
)
=
x
2
−
2
and let
f
(
n
)
(
x
)
f^{(n)}(x)
f
(
n
)
(
x
)
denote the
n
n
n
-th iteration of
f
f
f
. Let
H
=
{
x
:
f
(
100
)
(
x
)
≤
−
1
}
H=\{x:f^{(100)}(x)\leq -1\}
H
=
{
x
:
f
(
100
)
(
x
)
≤
−
1
}
. Find the length of
H
H
H
(the sum of the lengths of the intervals of
H
H
H
).
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