We define a function such that , and if there exists an integer such that , then is defined and if is odd if is even. What is the smallest

We define a function \(f(x)\) such that \(f(11)=34\), and if there exists an integer \(a\) such that \(f(a)=b\), then \(f(b)\) is defined and \(f(b)=3b+1\) if \(b\) is odd \(f(b)=\frac{b}{2}\) if \(b\) is even. What is the smallest possible number of integers in the domain of \(f\)?