A functional fix
Algebra
Level
5
Suppose \(f\) is a function from the positive integers to the positive integers that satisfies
\[ f(n) = \begin{cases} n - 600, & \text{ for } n > 2013,\\ f( f(n + 800)), & \text{ for } n \leq 2013. \\ \end{cases} \]
How many fixed points does \(f\) have?
Details and assumptions
A fixed point of a function \(f\) is a value \(x\) which satisfies \( f(x) = x \).
by
Calvin Lin