The inverse of the function `f(x)=(e^x-e^(-x))/(e^x+e^(-x))+2` is given by

Answer

`f^(-1)(x)=log_(e)((x-1)/(3-x))^(1//2)`

Explanation

`y=(e^(x)-e^(-x))/(e^(x)+e^(-x))+2=(e^(2x)-1)/(e^(2x)+1)+2`
or `e^(2x)=(1-y)/(y-3)=(y-1)/(3-y)`
or `x=(1)/(2)log_(e)((y-1)/(3-y))`
or `f^(-1)(y)=log_(e)((y-1)/(3-y))^(1//2)`
or `f^(-1)(x)=log_(e)((x-1)/(3-x))^(1//2)`