Functions, Relations & Transformations · Superchallenge problem

Let $a(x) = \dfrac1x$ and $b(x) = 1 - x$. Let $S$ be the set of all different functions that can be built by composing $a$ and $b$ with each other, in any order and any number of times (at least one use). Find the sum of $h(3)^2$ over all functions $h$ in $S$.