R⁺denotes the set of positive real numbers.

Determine all possible functions f:R⁺→ R⁺ such that:

f(f(x)) = 12x - f(x) for all x > 0.

(In reply to Explanation of my solution. by Chris, PhD)

if f(x) = ax + c, and a >0, and the function maps from R+ to R+, then c must be 0, because nothing would otherwise map into the interval (0,c].  

Posted by Steve Herman on 2012-09-10 08:46:21