What does "Good properties" mean? in my mathmatics skript the professor wrote:
"Warning: an inverse function does not automatically inherit all of the good properties of a function!" 
I don't really know what he means with "good". Are there bad properties of a function? This really drives me out of my mind at the Moment. I haven't found anything related to this on the Internet yet but I am still searching.
Thank you very much for your help.
FunkyPeanut
 A: A mathematical object is deemed good simply if it makes whatever you're trying to do easier. For example, often people refer to some functions as "nicely behaved." Thus, "good" is a fairly subjective term that can be relative to context. 
Note: you'll rarely have luck looking up the applications of colloquial language to mathematical ideas. Students need to understand and accept the fact that authors will sometimes use casual, nontechnical terminology. In fact, it's an important and necessary part of math to distill the formality and rigor into everyday conceptual ways of thinking about things.
To answer the more specific question about functions: there are many properties of functions that make them easier or just plain available at all to work with (in whatever area of math you happen to be working in), for example injective, surjective, piecewise continuous, continuous, differentiable, smooth, analytic, polynomial, compact support, conformal, holomorphic, homomorphic, etc. etc.
As an example, the inverse of a continuous function need not be continuous. If it is, then the function would be something called a homeomorphism in topology.
