arguments – How can I set a certain predicate for the result of a function to true?

I have an object called f (basically a vector of functions) and a predicate called MemberQR(actually its with subscript R).

MemberQR(f):=True I.e. I set the predicate to true.

Now I want to apply a Transformation on f, and the result still should have the predicate set to True.

So for fooFunction(f_?MemberQR):= 2 f; the result should also yield true when tested for MemberQR.

Of course, I do not know what exactly the components of f are, they might be different each time.

I have tried the use of % but was not sucessful. fooFunction is not supposed to produce output, it just transforms f.