The inverse of the function f(x)=ax−a−xax+a−x is

Let y=ax−a−xax+a−x=a2x−1a2x+1 ⇒y−1y+1=a2x−1−a2x+1a2x−1+a2x+1(Using componendo and dividendo)⇒y−1y+1=−22a2x⇒a2x=1+y1−y⇒2xloga⁡a=loga⁡1+y1−y⇒x=12loga⁡1+y1−y