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

Since, y=102x−1102×+1 ⇒  y102x+y=102x−1 ⇒  102x=1+y1−y ∴   2xlog1010=log101+y1−y ⇒  x=12log10(1+y1−y) Hence, the inverse of y is 12log10(1+y1−y) .