Could somebody help me to answer the following question?

Let $f:R_+ \rightarrow R_+$ be a nonindentically zero, nondecreasing, continuous, concave function with $f(0)=0$. Do we have that for any $s,t \in [0,1]$,

$$f(x)f(stx)\leq f(sx)f(tx), \quad \forall x \geq 0.$$

or equivalently, do we have that for any $t\in (0,1)$, $\frac{f(x)}{f(tx)}$ is nonincreasing on $x >0$.

Thanks!