question_answer

If \[a\,f(x)\,+b\,f\left( \frac{1}{x} \right)=x-1,x-1,x\ne 0\]and \[a\ne b\], then f(2) is equal to

A)  \[\frac{a}{{{a}^{2}}-{{b}^{2}}}\]    

B)  \[\frac{(a+2b)}{2({{a}^{2}}-{{b}^{2}})}\]

C)  \[\frac{(a-2b)}{({{a}^{2}}-{{b}^{2}})}\]       

D)  \[\frac{(2a+b)}{2({{a}^{2}}-{{b}^{2}})}\]