The main purpose of this paper is to characterize norm-additive in modulus, not necessarily linear, maps defined between function algebras (not necessarily unital or uniformly closed). In fact, for function algebras $A$ and $B$ on locally compact Hausdorff spaces $X$ and $Y$, respectively, we study surjections $T, S:A\longrightarrow B$ satisfying $\||Tf|+|Sg|\|_Y= \||f|+|g|\|_X$ for all $f,g\in A$.
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