Let (V,0) be a germ of an (analytic) singularity in \((k^ t,0)\) and \(f_ 0: (k^ s,0)\to (k^ t,0)\) an (analytic) germ function. The author studies properties of \((f^{-1}(V),0)\), which will be noted by \((X_ 0,0)\), from the Thom-Mather point of view via the action of a certain subgroup \(K_ V\) of the contact group on the space of sections \(f_ 0\). He proves that if \(f_ 0\) has finite \(K_ V\)-codimension, (V,0) algebraic implies \((X_ 0,0)\) algebraic, and when \(f_ 0\) is weighted homogeneous the topological triviality for deformations of nonnegative weight of \((X_ 0,0)\), and gives some consequences of this to the study of versal deformations of \((X_ 0,0)\). Also the author applies this result to weighted homogeneous isolated Gorenstein singularities and extends results of \textit{E. Looijenga} [Topology 16, 257-262 (1977; Zbl 0373.32004)] and \textit{K. Wirthmüller} [``Universell topologische triviale Deformationen'' (Thesis, Univ. Regensburg)] about topological triviality results for versal deformations.