If 2f(x)+3f(1/x)=x-1 , then find f(x)

Answers (1)

Solution:  We have ,

                    2f(x)+3f(frac1x)=x-1

             Put     frac1x in place of x

         Rightarrow      2f(frac1x)+3f(x)=frac1x-1=frac1-xx

                     f(frac1x)+frac32f(x)=frac1x-1=frac1-x2x      .......(1)

        Rightarrow        frac23f(x)+f(frac1x)=fracx-13         ......(2)

        From (1) and (2) we get   f(x)=-frac3(2x+3)(x-1)5x

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