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