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Prove / disprove: if $f(n)=O(g(n))$ then $2^{f(n)}=O (2^{g(n)})$

This is related to: Big-O: If $f(n)=O(g(n))$, prove $2^{f(n)}=O(2^{(g(n)})$

But I don't see how the answer there is right (I commented on that there) and I have a question about a different approach.

Can we use that since $2^x$ is a continuous positive function then it keeps signs of inequalities? i.e $a<b$ then $2^a<2^b$?

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shinzou
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  • Note that $2^{ab}\neq 2^a 2^b$ – Ben Grossmann Oct 26 '15 at 14:46
  • @Omnomnomnom yeah I see it now... – shinzou Oct 26 '15 at 14:47
  • @Did From the duplicate auto-text: If those answers do not fully address your question, please ask a new question. That's exactly what this question did, and it shouldn't have been closed as a result. – Ben Grossmann Oct 26 '15 at 14:47
  • @Omnomnomnom Yes it ought to, since it was asking for an explanation about a posted answer and the right move was to first ask for it there, then wait a little, and then, if nothing came, to post a new question. Please see the delay between the comment asking for explanation there being posted and being answered. – Did Oct 26 '15 at 14:50
  • I assumed David is from a different time zone, so the answer would probably come tomorrow for me and I had another question about this too so the answer didn't fully address my question. It doesn't matter now though. @Did – shinzou Oct 26 '15 at 14:52

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