Question

If a*f(x) + b*f(1/x) = 1/x - 5 then find f(x).

Answer 1

a  f(x) + b  f(1/x) =  1/x   -  5             or  is  it   1/(x - 5)  ??

a f(1/x) + b f (x) =  x - 5          substituting x in place of 1/x

solving the two equations. : 
     ( a^2 - b^2 )f(x) =  a/x  - 5a  - b x +5b
 
f(x) =  [ a/x + 5 (b -a) - b x ] /(a^2 - b^2)

Answer 2

a  f(x) + b  f(1/x) =  1/x   -  5             or  is  it   1/(x - 5)  ??

a f(1/x) + b f (x) =  x - 5          substituting x in place of 1/x

solving the two equations. :

    ( a^2 - b^2 )f(x) =  a/x  - 5a  - b x +5b

f(x) =  [ a/x + 5 (b -a) - b x ] /(a^2 - b^2)

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