The inverse of the function y=10x−10−x10x+10−x+1 is:

We have, y=10x−10−x10x+10−x+1 ⇒          y−1=102x−1102x+1 ⇒          y−1+1y−1−1=102x−1+102x+1102x−1−102x−1                               [Using componendo and dividendo]⇒          yy−2=2.102x−2  ⇒  y2−y=102x ⇒        2x=log10 ( y2−y) ⇒        x=12log10 ( y2−y)=f−1(y) Hence, the inverse of the given function is  y=12log10 ( x2−x)