# Another functional equation

• October 19th 2008, 07:37 AM
alexmahone
Another functional equation
Let $X$ be the set of all positive integers greater than or equal to $8$ and let $f: X \to X$ be a function such that $f(x + y) = f(xy)$ for all $x \ge 4, y \ge 4$. If $f(8) = 9$, determine $f(9)$.
• October 19th 2008, 09:25 AM
Moo
Hello,
Quote:

Originally Posted by alexmahone
Let $X$ be the set of all positive integers greater than or equal to $8$ and let $f: X \to X$ be a function such that $f(x + y) = f(xy)$ for all $x \ge 4, y \ge 4$. If $f(8) = 9$, determine $f(9)$.

$f(9)=f(5+4)=f(20)=f(16+4)=f(64)$

$f(8)=f(4+4)=f(16)=f(8+8)=f(64)$

Hence $f(8)=f(9)$