This problem should not be tough for university Math students after learning the concept of even functions and odd functions.
An even function is one that . An example will be
An odd function is one that . And example will be
So how to we prove the symmetry with this concept, consider a simple function , it is obvious that its symmetrical about y-axis. from the graph. But how did we know or tell. First, we know that and , etc. Thus we know that which brings us back to the idea of even function. Students need to attempt to write out this particular relationship mathematically. Such notations help them to express their ideas much clearly and also assists the examiners to mark, instead of trying to read through a long chunk of explanation.
Now, here is a problem for students, how do we prove that a function is symmetrical about x-axis?