If f(x)=(alpha x+1), alpha is not equal to 0 , is the inverse of itself ,then the value of alpha is

Answers (1)

Solution:    We have ,   f(x)=(alpha x+1),

                     y=(alpha x+1)        ........(1)

                  Rightarrow        x=fracy-1alpha Rightarrow f^-1(y)=(fracy-1alpha ),

                 or             f^-1(x)=(fracx-1alpha )          ..........(2)

               Now  ,    f^-1(x)=f(x)   gives

                           (fracx-1alpha )=(alpha x+1)       ........(3)

                 This equation is obviously satisfied by alpha =-1

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