Find the function

[Guest]

Hello, could you help me??

Let the function
$f : (0,+\infty) \rightarrow(0,+\infty)$

we know that:

• $f(xy)= f(xf(\frac{1}{y}))$ for all x,y>0

•$\lim_{x \to ĥ+\infty}f(x)=0$


Find the $f(x)$

[spinos]

Hello, could you help me??

Let the function
$f : (0,+\infty) \rightarrow(0,+\infty)$

we know that:

• $f(xy)= f(xf(\frac{1}{y}))$ for all x,y>0

•$\lim_{x \to +\infty}f(x)=0$


Find the $f(x)$