Assume f(x) = ax
Then a*ax = 12x - ax
a = 3 or -4
but f(x) = -4x does not map positives to positives. Thus, a must = 3.
Assume f(x) = b/x
Then x = 12x - b/x
There is no value of b such that this equation works for all x. Therefore, f(x) is not of the form b/x.
I think that the same is true if f(x) = ax^b where b <> 1
I have not exhausted all functions that map R+→ R+ ,
but I suspect that the only solution is f(x) = 3x