I thought of this and I think it is interesting to see how it can be solved using elementary calculations.

What is the line of symmetry of f(x) = arctan(x)+arctan(6-x)?

Seems scary? It requires no calculus. arctan works nicely because it makes a graphic picture that is easy to see, but other functions will work as well.

Here is a list of questions that lead to the solution:
How does f(6-x) compare to f(x)?

Using the previous question, given a point (x,y) on the curve, what is another point on the curve?

What is the midpoint of the two points?