2011/031) If f(x) + 2f(2002/x) = 3x then find f(2)?

ans: this type of problem we need to eliminate f(2002/x)and put x = 2

(x) + 2f(2002/x) = 3x --- 1
we realize that x and 2002/x are reciprocal so putting 2002/x for x we get

f(2002/x) + 2 f(x) = 3(2002/x) ... 2

multiply 2nd by 2 and subtract (1) fom it

3 f(x) = 6(2002/x) - 3 x

or f(x) = 4004/ x - x

putting x = 2 we get

f(2) = 2000