  Let $h \geq 2$, $k \geq 5$ be integers and $A$ be a nonempty finite set of
$k$ integers. Very recently, Tang and Xing studied extended inverse theorems
for $hk-h+1 < \left|hA\right| \leq hk+2h-3$. In this paper, we extend the work
of Tang and Xing and study all possible inverse theorems for
$hk-h+1<\left|hA\right| \leq hk+3h-4$. Furthermore, we give a range of $|hA|$
for which inverse problems are not possible.
