Prove that if $f$ is monotone decreasing on $(a,b)$ then $g=-f$ is monotone increasing on $(a,b)$.
This question is in the book "Introduction to Mathematical Analysis" by W.R Parzynski and P.W. Zipse. Most of the answers that I've found in the internet use derivative to determine if the function is monotone increasing or monotone decreasing. However, it was not stated in the book. So, it means that I'm limited to the definition in proving the exercise. Can someone help me since I'm lost and I don't even know how to start my proof. Thanks for helping in advance.