2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167981We study the exact extremal orders of compositions $f(g(n))$ of certain arithmetical functions, including the functions $σ(n)$, $ϕ(n)$, $σ^*(n)$ and $ϕ^*(n)$, representing the sum of divisors of $n$, Euler's function and their unitary analogues, respectively. Our results complete, generalize and refine known results.improved and corrected final versionNumber Theory11A25, 11N37text