function analysis question

[jte]

I'm not exactly sure what you mean by "not feasible to do so for more complex functions". Exact solutions are generally only possible for restricted classes of problems. They can, of course, be extremely useful when they're available.

When looking at exact solutions over multiple dimensions, a typical way of improving one's understanding is to … graph the solution set. A trivial toy example would be something like ASIN(2*COS(X*X-Y*Y))+ASIN(2*SIN(X*X+Y*Y)) with real (not complex) arithmetic. The graph of that <9^9^9 gives one a quick understanding of the (bulk of the) domain; now try writing down an explicit expression for the domain.