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I believe the original question said:
a character belongs to a list/array of invalid characters
and not:
belongs to a null-terminated string
which, if it did, then strchr would indeed be the most suitable answer. If, however, there is no null termination to an array of chars or if the chars are in a list structure, then you will need to either create a null-terminated string and use strchr or manually iterate over the elements in the collection, checking each in turn. If the collection is small, then a linear search will be fine. A large collection may need a more suitable structure to improve the search times - a sorted array or a balanced binary tree for example.
Pick whatever works best for you situation.