By "function implementation files" do you mean .h or .cpp files? (Usually I call .cpp files "implementation" files, and .h files call "interface" files.)
If you mean .cpp files, then of course. This is where you usually see using namespace std . This means that all the code in this .cpp file has access to std without qualification.
If you mean .h files, you can, but you shouldn't. If you include it in an .h file, it will automatically apply to any .cpp file that contains an .h file that can contain many files. Typically, you do not want to tell other modules which namespaces to import. It is best to put it in every .cpp file, rather than in a regular .h file.
Edit: User @lachy suggested editing, which I wonโt include verbatim, but they suggested I point out that using namespace std usually considered bad practice due to pollution of the namespace. They gave a link to a question on this topic: Why is "using the std namespace;" considered bad practice?
mgiuca
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