2001 AMC 12 Problem 9

Problem 9 of 25EasierAlgebra

Let

f

be a function satisfying

f(xy) = \dfrac{f(x)}{y}

for all positive real numbers

x

and

y.

f(500) = 3,

what is the value of

f(600)?

Show solution

Solution

Choose

x = 500

and

y = \dfrac{6}{5}

so that

xy = 600.

Then

f(600) = \dfrac{f(500)}{\frac{6}{5}} = \dfrac{3}{\frac{6}{5}} = \dfrac{5}{2}.

Thus, the correct answer is C.

Concepts: functional equation · substitution

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.