+145 We define a function \(f(x)\) such that \(f(14)=7\), 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 \(f\)?
+9466 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 and f(b) = b/2 if b is even .
We must have at least these defined values of the function:
f(14) = 7
f(7) = 22
f(22) = 11
f(11) = 34
f(34) = 17
f(17) = 52
f(52) = 26
f(26) = 13
f(13) = 40
f(40) = 20
f(20) = 10
f(10) = 5
f(5) = 16
f(16) = 8
f(8) = 4
f(4) = 2
f(2) = 1
f(1) = 2
There must be at least 18 integers in the domain of f .
