I have two (strictly) positive functions $f(x)$ and $g(x)$ defined on $\mathbb{R}$. I am required to show that $f(x) \leq O(g(x))$ for $x \to \pm \infty$. I showed that $f(x) \leq kg(x)$ for $|x| \to \infty$. Is this enough ?
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1I've never seen $f(x) \leq O(g(x))$ before. – zhw. Jan 21 '16 at 02:20
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Perhaps $\le$ is due to the misconception that $O(g) = \Theta(g)$. – Reinstate Monica Jan 21 '16 at 02:54
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It's not clear to me what is meant by "for $x \rightarrow \dots", but this looks pretty close to the definition of $O(g(x))$, so OP likely has it mostly right but maybe an answerer will help explain the concepts. – Dan Brumleve Jan 21 '16 at 04:05