does there exist 2 functions that are not monotonic and at the same time their subtraction is monotonic.and also if we multiply one by the other we get another we also get another monotonic function, their division should be monotonic too(whether we are dividing function 1 by function 2 or dividing function 2 by function 1, we should get a monotonic answer on both processes).these 3 conditions should be satisfied.I would be glad someone helps me.
2026-04-02 13:24:15.1775136255
find two non-monotonic functions which their subtraction, multiplication and division are monotonic.
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Consider the function taking value $-1$ at all non-zero numbers and $1$ at $0$. Consider it with itself. It is not monotonic and the difference, product and ratio of these functions is trivially monotonic.
Hope it helps:)