Question about continuity and absolute value

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If $f_1(x)$, $f_2(x)$, ..., $f_n(x)$, are continuous functions, then $$ \sum_{\textrm{some }i} |f_i(x)| + \prod_{\textrm{some }i} |f_i(x)| $$ is continue? If a such theorem exists, it would be useful in finding maxima and minima of some functions.