Let K be a compact Hausdorff space, $mathfrak{A}$ a commutative complex Banach algebra with identity and $mathfrak{C}(mathfrak{A})$ the set of characters of $mathfrak{A}$. In this note, we study the class of functions $f:K{ ightarrow}mathfrak{A}$ such that ${Omega}_{mathfrak{A}}{circ}f$ is continuous, where ${Omega}_{mathfrak{A}}$ denotes the Gelfand representation of $mathfrak{A}$. The inclusion relations between this class, the class of continuous functions, the class of bounded functions and the class of weakly continuous functions relative to the weak topology ${sigma}(mathfrak{A},mathfrak{C}(mathfrak{A}))$, are discussed. We also provide some results on its completeness under the norm defined by ${mid}{parallel}f{parallel}{mid}={parallel}{Omega}_{mathfrak{A}}{circ}f{parallel}_{infty}$.