How are the increasing and decreasing intervals of a function and it’s reciprocal related?

Answer 1

if f (a) and f(b) are positive, then
increasing means that if a<b then f(a) < f(b)
so 1/f(a) > 1/f(b)
so 1/f(x) is decreasing

Explore what happens when a or b or both are negative.
maybe a good online graphing site would be useful at this point to check your conclusions.

Or, if you have calculus, compare the derivatives.