Difference between revisions of "2001 AMC 12 Problems/Problem 9"
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== Problem == | == Problem == | ||
− | Let <math>f</math> be a function satisfying <math>f(xy) = \frac{f(x)}y</math> for all positive real numbers <math>x</math> and <math>y</math> | + | Let <math>f</math> be a function satisfying <math>f(xy) = \frac{f(x)}y</math> for all positive real numbers <math>x</math> and <math>y</math>. If <math>f(500) =3</math>, what is the value of <math>f(600)</math>? |
<math>(\mathrm{A})\ 1 \qquad (\mathrm{B})\ 2 \qquad (\mathrm{C})\ \frac52 \qquad (\mathrm{D})\ 3 \qquad (\mathrm{E})\ \frac{18}5</math> | <math>(\mathrm{A})\ 1 \qquad (\mathrm{B})\ 2 \qquad (\mathrm{C})\ \frac52 \qquad (\mathrm{D})\ 3 \qquad (\mathrm{E})\ \frac{18}5</math> | ||
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== Solution == | == Solution == | ||
<math>f(500\cdot\frac65) = \frac3{\frac65} = \frac52</math>, so the answer is <math>\mathrm{C}</math>. | <math>f(500\cdot\frac65) = \frac3{\frac65} = \frac52</math>, so the answer is <math>\mathrm{C}</math>. | ||
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+ | == See Also == | ||
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+ | {{AMC12 box|year=2001|num-b=8|num-a=10}} |
Revision as of 07:04, 15 February 2009
Problem
Let be a function satisfying for all positive real numbers and . If , what is the value of ?
Solution
, so the answer is .
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |