Let \(f\) be a real-valued function defined on the integers in the interval \([1,n-1]\), and let \(G\) be a graph with \(n\) non-isolated vertices. The concept of the local value of a degree-function index was introduced by Rada in [Local value of a vertex-degree function index of a graph, MATCH Commun. Math. Comput. Chem. 95 (2026) 111-124]. The degree-function index \(H_f(G)\) is defined by \[H_f(G)=\sum_{u\in V(G)} f(d_G(u)),\] where \(d_G(u)\) denotes the degree of the vertex \(u\) in \(G\). The local value of \(H_f\) at a vertex \(u\), denoted by \(f_G(u)\), measures the contribution of \(u\) to the total value of the index. In the same paper, Rada posed four questions concerning the local value of a degree-function index and the zeroth-order general Randić index.
In this paper, we provide answers to these questions. We establish an upper bound for the difference between the local values of a vertex-degree function index \(f\) at a vertex \(u\) in a graph \(G\) and in an induced subgraph \(H\) of \(G\). Furthermore, we derive an upper bound for the difference between the local values of \(f\) at two vertices of a graph \(G\). We also obtain some upper and lower bounds for the zeroth-order general Randić local value \(({\mathcal R}_{\alpha})_G(u)\). As applications of these results, we identify the vertices attaining the maximum local value of the zeroth-order general Randić index \({\mathcal R}_{\alpha}\) for \(0<\alpha<1\), and the minimum local value for \(\alpha<0\). Finally, we present some concluding remarks and discuss several possible directions for future research.