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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

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    $f:\mathbb{R}\to +\infty$ what does it mean?2012-11-18

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