Yes, although it might not be a very useful function. However, there are times when you are studing properties of a set of functions and it is quite possible that a member of a set of functions has a null domain.
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There are two sets for any given function, the domain and the range. The range is the set of outputs and the set of inputs is the domain.
Domain is a set in which the given function is valid and range is the set of all the values the function takes
It is the set which comprises the inputs to a function.
The domain is a subset of the values for which the function is defined. The range is the set of values that the function takes as the argument of the function takes all the values in the domain.
The domain is the set of values of the input while the range is the set of output values.