Hey guys, I've been working on the topic of monotonicity, and I've got a bit of a grasp on using the definitions of strictly/monotonically increasing/decreasing to show which category a function falls into, but this one is slipping me, because it's not so much a composite function as a modification of an existing function...

I want to say that the monotonicity is reverse and that $\displaystyle h(x)$ is monotonically increasing, because with reciprocal functions, where $\displaystyle g(x)$ was small, $\displaystyle h(x)$ will be large, and where $\displaystyle g(x)$ was large, $\displaystyle h(x)$ will be small.Given that $\displaystyle g(x)$ is negative and monotonically decreasing, what can be said about the monotonicity of: $\displaystyle h(x)=\frac{1}{g(x)}$?

If that's even right, I'm not sure how to write the proof when I only have the definition in terms of 1 function, $\displaystyle g(x)$.

Any ideas?