Final answer:
The cosine function (cos(x)) is an eigenfunction of both the coordinate and reflection operators because of its even symmetry, fulfilling the criteria set by the student's question in the context of quantum mechanics. Option C is correct.
Step-by-step explanation:
The student is clearly asking about concepts that are relevant to quantum mechanics, a subject area within physics. Specifically, the student is asking for which function among the given options is an eigenfunction of both the coordinate (position) operator and the reflection (parity) operator. This is a concept applicable to wave functions in quantum mechanics.
The eigenfunction of the coordinate operator in the position representation can be any reasonable function because the position operator acts simply as a multiplication by x, while eigenfunctions of the reflection operator must display symmetry or antisymmetry when their argument gets replaced by its negative.
From the given options, the cosine function (cos(x)) is the correct answer since it is even under reflection, i.e., cos(-x) = cos(x), and also gets multiplied by a scalar upon the action of the coordinate operator. Functions such as sine, exponential functions, and polynomials of even degree can also be eigenfunctions under certain conditions, but with respect to the way the question is asked and the information given, the cosine function is the eigenfunction satisfying the criteria.