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Omni-MATH / Let f(x)=x²−2 and let f^((n))(x) denote the n-th iteration of f. Let H={x:f^((100))(x)≤−1}. Find the length of H (the sum of the lengths of the intervals of H).

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problem

Let f(x)=x2−2f(x)=x^2-2 and let f(n)(x)f^{(n)}(x) denote the nn-th iteration of ff. Let H={x:f(100)(x)≤−1}H=\{x:f^{(100)}(x)\leq -1\}. Find the length of HH (the sum of the lengths of the intervals of HH).
Plain-text mathematical notation (without MathML)
Let f(x)=x²−2 and let f^((n))(x) denote the n-th iteration of f. Let H={x:f^((100))(x)≤−1}. Find the length of H (the sum of the lengths of the intervals of H).
Original LaTeX notation
Let $f(x)=x^2-2$ and let $f^{(n)}(x)$ denote the $n$-th iteration of $f$. Let $H=\{x:f^{(100)}(x)\leq -1\}$. Find the length of $H$ (the sum of the lengths of the intervals of $H$).

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Source and history

task_id
76f9022d-035b-5546-81c5-95508a767720
task_key
test--76f9022d-035b-5546-81c5-95508a767720
task_revision_id
1
config / split
/ test

Official source

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