# function f satisfies f(xy) = f(x)/y , f(30) = 20. Find f(40)

The function $f$ satisfies

$$f(xy) = \frac{f(x)}y$$

and $f(30) = 20$.

Find $f(40)$.

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HINT: $40=30\cdot\dfrac43$. –  Brian M. Scott May 9 '12 at 17:55

$f(40) = f(30 \cdot 4/3) = f(30) \cdot 3/4 = 15$

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More generarily $f(x)= f(30)*30/x$ –  N. S. May 9 '12 at 17:56
While this gives the solution to the problem, it's also worth noting that $f(x)=f(1\cdot x)=f(1)/x$. The conditions of the problem mean $f(1)/30=20$, so $f(1)=600$ and $f(x)=600/x$. –  Aaron May 9 '12 at 17:58