MHB Solving for $f(600)$ Given $f(500)=3$

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The function f satisfies the property f(xy) = f(x)/y for all x, y > 0, and it is given that f(500) = 3. To find f(600), x is set to 500 and y is calculated as 600/500, which equals 6/5. This leads to the calculation f(600) = f(500)/(6/5), resulting in f(600) = 5/2. The discussion highlights the simplicity of the solution, with participants expressing surprise at the straightforwardness of the problem.
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given a function $f$, satisfying :
(1) $f(xy)=\dfrac {f(x)}{y}$ for all $x,y>0$
(2) $f(500)=3$
what is the value of $f(600)$
 
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Albert said:
given a function $f$, satisfying :
(1) $f(xy)=\dfrac {f(x)}{y}$ for all $x,y>0$
(2) $f(500)=3$
what is the value of $f(600)$
Is this a trick question or did I just stumble upon a quick way to do this? I usually go insane when you post one of these.

[sp]
[math]f(xy) = \frac{f(x)}{y}[/math]

Let x = 500 and xy = 600. Then y = 600/500 = 6/5.

Thus
[math]f(600) = \frac{f(500)}{\frac{6}{5}} = \frac{3}{\frac{6}{5}} = \frac{5}{2}[/math]
[/sp]

-Dan
 
topsquark said:
Is this a trick question or did I just stumble upon a quick way to do this? I usually go insane when you post one of these.

[sp]
[math]f(xy) = \frac{f(x)}{y}[/math]

Let x = 500 and xy = 600. Then y = 600/500 = 6/5.

Thus
[math]f(600) = \frac{f(500)}{\frac{6}{5}} = \frac{3}{\frac{6}{5}} = \frac{5}{2}[/math]
[/sp]

-Dan
please don't go insane,your answer is correct,thanks for participating.
By the way ,do you prefer more challenging problems (need a lot of tricks)?
 
Albert said:
please don't go insane,your answer is correct,thanks for participating.
By the way ,do you prefer more challenging problems (need a lot of tricks)?
I don't usually lack self-confidence but whenever I can quickly answer a problem from you or the POTWs I get the feeling I've overlooked a critical point! Like this one...I wasn't expecting a one line solution so I was unsure about it. Personally I prefer the challenge, though I usually don't post my attempts. I like these. (Yes)

-Dan
 
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