One-way Trapdoor Function

Do the functions of the collatz conjecture and their inverses model a Trapdoor Function?

That is, given f(n) = n/2 or 3n+1 and the inverse g(n)=2n and (n-1)/3 it is easy to go from 42 to 1 by repeating the steps but it requires a nondeterministic Turing machine to find g(42).