function f satisfies f(xy) = f(x)/y , f(30) = 20. Find f(40)
0
$\begingroup$
The function $f$ satisfies
$f(xy) = \frac{f(x)}y$
and $f(30) = 20$.
Find $f(40)$.
functionsrelations
asked 2012-05-09
user id:30997
4
22bronze badges
1
HINT: $40=30\cdot\dfrac43$. – 2012-05-09
1 Answers
1
4
$f(40) = f(30 \cdot 4/3) = f(30) \cdot 3/4 = 15$
asked 2012-05-09
user id:4891
132
88bronze badges
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