Given functions $a$ and $b$ ; $a,b: \mathbb{R} \rightarrow \mathbb{R}$
find a set of functions $F$ so that
$f \in F \Rightarrow \forall t \in \mathbb{R} . f(a(t),b(t)) = 1$
does this set always have elements for every $a$ and $b$?
Is there only 1?
If there are more than 1 is there a pattern?