Can all quasiconvex functions be represented as a ratio of a convex function and a concave function?

Question

My optimization algorithms teacher raised this conjecture:

$\forall f:D\subset\mathbb{R}^n\rightarrow \mathbb{R}$ quasiconvex $\exists (p, q)$ where

$p:D\rightarrow \mathbb{R}$ convex,

$q:D\rightarrow \mathbb{R}$ concave with $q(x)>0~\forall x\in D$

such that

$$f(x) = \frac{p(x)}{q(x)}$$