I have the following problem:
$f: \mathbb R\to +\infty $ and $f(x) - f(y) = f( x / y) , x,y > 0 $
a)Show that $f(1) = 0$ b)Show that $f$ is one-to-one and that $f(x)=0$ has a single solution
c)solve the equation $ f(x^2 -2) + f(x) = f(5x -6) $
d) If $f(x) > 0$ for every $x>1$, show that $f$ is strictly increasing at $(0, +\infty) $
Thank you