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Mar 24, 2010 at 20:45 comment added Sergei Ivanov I added an example where all coefficients are positive.
Mar 24, 2010 at 20:43 history edited Sergei Ivanov CC BY-SA 2.5
added example with all coefficients positive
Mar 24, 2010 at 19:25 comment added Sergei Ivanov $f(x)=2x+1$ does.
Mar 24, 2010 at 19:19 comment added darij grinberg This was basically said in the comments to the question. $f$ must send $\left[0,\infty\right)$ to a proper subset of $\left[0,\infty\right)$.
Mar 24, 2010 at 19:19 comment added Michael Lugo Perhaps one needs the condition that $f$ and $g$ have nonzero constant term.
Mar 24, 2010 at 18:56 history edited Sergei Ivanov CC BY-SA 2.5
deleted 26 characters in body
Mar 24, 2010 at 18:51 history answered Sergei Ivanov CC BY-SA 2.5