Functions: f(x*y) = f(x) * f(y) f(x) different 0 , ofr every x,y E Df, etc

[gotham1]

f : +infinity --> R

Data:

f(x*y) = f(x) * f(y)
f(x) different 0 , ofr every x,y E Df
f(x) < 1 , x>1
f(1)=1, x >0
f(1/x) 1/f(x) , x> 0

You have to proove :

a) f (x) > 0 , x>0
b) f monotonically decreasing in Df
c) f (e-x+2) = f ( 1/4x) * f ( x^2 +2x ) it has only 1 possitive solution