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Quantum Numbers

Let f be a ...

Question

Let $f$ be a real valued function such that $f (x) + 2 f (\frac{2002}{x}) = 3 x$ for all $x > 0$ . Find $f (2)$

A

1000

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B

2000

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C

3000

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D

4000

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Solution

The correct option is B $2000$
Put $x = 1001$
$f (1001) + 2 f (2) = 3003 \dots \dots (1)$
Put $x = 2$
$f (2) + 2 f (1001) = 6 \dots \dots (2)$
Hence $f (2) = 2000$

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