# Prove that the negative of monotone decreasing function is monotone increasing [closed]

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.

## closed as off-topic by Shailesh, mechanodroid, Henrik, Guy Fsone, mlcNov 4 '17 at 20:29

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• welcome to maths stack exchange. In future post, kindly include what you have tried in your post. We usually dislike quesiton that tell us what to do. here is a link to show us how to use mathjax to type maths on this site. – Siong Thye Goh Nov 4 '17 at 3:46
• Oh, sorry about that. I will not do it again in the future. Thanks for pointing out. – xxdy Nov 4 '17 at 4:05

monotone decreasing means that if $x > y$, $f(x)-f(y) < 0$.
$$f(x)-f(y) < 0$$
Multiply by $-1$.
$$-(f(x)-f(y)) > 0$$