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Let $f:\mathbb{R} _{+}\rightarrow \mathbb{R} _{+}$ be a real function.

Find all conditions on $f$ under which

$f$ is convex on $\left( a;b\right) \subset \mathbb{R} _{+}$$\Leftrightarrow$ $\dfrac {1} {f}$ is convex on $\left( a;b\right) \subset \mathbb{R} _{+}$

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    Correction: You can have neither $f$ nor $1/f$ convex if $f$ is highly irregular, e.g. have intervals where it is nowhere differentiable. Is that the type of conditions you are looking for?2012-08-30

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