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Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) = g(x) E O(f(x))

Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) = g(x) E O(f(x))

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) → g(x) E O(f(x))
Transcribed Image Text:Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) → g(x) E O(f(x))
Expert Solution
Step 1: Given.

Big-Θ notation: A function g(n) is in Θ(f(n)) if there exist constants c1, c2, and N such that c1|f(n)| ≤ |g(n)| ≤ c2|f(n)| for n>N.

Given: f and g are positive constants.

∀f, g:ℕ→ℝf(x)∈Θgx ⇒gx∈Θfx

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