SOLUTION: Suppose a function {{{f}}} is such that {{{f(1/x)-3f(x)=x}}} for every x≠0(x that does not equal 0). Find {{{f(2)}}}.

Write the given functional equation for x = 2 and for x = 1/2.


For x = 2, you will have

    f(1/2) - 3f(2) = 2              (1)


For x = 1/2, you will have

    f(1/(1/2)) - 3f(1/2) = 1/2,  

or

    f(2) - 3f(1/2) = 1/2.           (2)


Let  u = f(1/2),  v = f(2)  for breavity.  Then you can re-write (1) and (2) in the form

    u - 3v = 2                       (3)
    
    v - 3u = 1/2                     (4)


Now I want to solve the system of linear equations (3) and (4) and find v.


For it, I express  u = 2+ 3v  from (3) and substitute it into equation (4)

    v - 3*(2+3v) = 1/2.


In the last equation, multiply both sides by 2 to run from denominator

    2v - 6*(2+3v) = 1


Simplify and find v

    2v - 12 - 18v = 1

        -16v      = 1 + 12

        -16v      =   13

           v      =   .


Thus  v = f(2) = ,  and the problem is just solved.


ANSWER.  f(2) = .