Let $\varphi (z)=z^d+c$ be a polynomial over a field $K.$ We study the inverse stability of $\varphi (z)$ over $K.$ In this paper, we establish some sufficient conditions for the inverse stability of $\varphi (z)$ over the field of rational numbers and a function field. Furthermore, we also provide necessary and sufficient conditions for the inverse stability of $\varphi (z)$ over a finite field.