Question

Let f be a real valued function such that f(x)+2f(2002/x)=3x for all x>0. Find f(2)

Answer 1

Answer :

Given, f(x) + 2f(2002/x) = 3x and x > 0

We put x = 2. Then,

f(2) + 2f(2002/2) = 3 × 2

⇒ f(2) + 2f(1001) = 6 ...(i)

Again, we put x = 1001. Then,

f(1001) + 2f(2002/1001) = 3 × 1001

⇒ f(1001) + 2f(2) = 3003

⇒ 2f(1001) + 4f(2) = 6006,
multiplying both sides by 2

⇒ 6 - f(2) + 4f(2) = 6006, by (i)

⇒ 3f(2) = 6006 - 6

⇒ 3f(2) = 6000

⇒ f(2) = 2000

∴ f(2) = 2000

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