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The function $f$ satisfies

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

and $f(30) = 20$.

Find $f(40)$.

  • 1
    HINT: $40=30\cdot\dfrac43$.2012-05-09

1 Answers 1

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

  • 2
    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 $f(x)=600/x$.2012-05-09