The inverse of the function f(x) =ex−e−xex+e−x+2 is given by :

Let y=f(x) =ex−e−xex+e−x+2 ⇒             y−2=e2x−1e2x+1 ⇒ (y−2)e2x+(y−2)=e2x−1⇒             (y−3) e2x=−y+1⇒e2x=1−yy−3⇒e2x=y−13−y⇒2x=loge(y−13−y)=f−1(y)=loge(y−13−y)12⇒f−1(x)=loge(x−13−x)12