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  • The inverse of the function f(x)=1+(e^x -e^-x /e^x+e^-x) , x is not equal to 0 and 2 , is

The inverse of the function f(x)=1+(e^x -e^-x /e^x+e^-x) , x is not equal to 0 and 2 , is

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Solution:      We have ,

                       f(x)=frace^x-e^-xe^x+e^-x

              Rightarrow           e^2x=fracy2-y

             Rightarrow       f^-1(y)=x=frac12ln fracy2-y

          \ Rightarrow f^-1(x)=frac12ln fracx2-x.

Posted by

Deependra Verma

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