Convexity conditions for $f$ and $\dfrac {1} {f}$

Question

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 $\left( a;b\right) \subset \mathbb{R} _{+}$