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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 \(f\)?

DanielCai Jun 28, 2018

#1**+2 **

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 .

hectictar Jun 29, 2018