2002 AMC 12P Problems/Problem 20

Problem

Let $f$ be a real-valued function such that

$f(x) + 2f(\frac{2002}{x}) = 3x$

for all $x>0.$ Find $f(2).$

$\text{(A) }1000 \qquad \text{(B) }2000 \qquad \text{(C) }3000 \qquad \text{(D) }4000 \qquad \text{(E) }6000$

Solution

When $x = 2$ , then we get $f(2) + 2f(1001) = 6$ ; we can also substitute $x$ as $1001$ , then we will get $f(1001) + 2f(2) =3003$ . Solve this system of equations, then we get $f(2)= 2000$ $\Longrightarrow \boxed{\mathrm{B}}$ .

2002 AMC 12P (Problems • Answer Key • Resources)
Preceded by Problem 19	Followed by Problem 21
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

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2002 AMC 12P Problems/Problem 20

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