For which function is f(x) equal to f^-1(x)? f(x)=x+6x−6 f(x)=x+2/x−2 f(x)=x+1/x−1 f(x)=x+5/x−5

We will find the inverse of the given functions:
 y = x + 2 / x-2
 (x-2) y = x + 2
 -2y + xy = x + 2
 -2y + xy = x + 2
 x (y - 1) = 2 + 2y
 x (y - 1) = 2 (y + 1)
 x = 2 (y + 1) / (y - 1)
 f (x) ^ - 1 = 2 (x + 1) / (x - 1)
 The inverse is different.
 f (x) = x + 1 / x-1
 y = x + 1 / x-1
 (x-1) y = x + 1
 -y + xy = x + 1
 x (y - 1) = 1 + y
 x (y - 1) = (y + 1)
 x = (y + 1) / (y - 1)
 f (x) ^ - 1 = (x + 1) / (x - 1)
 The inverse is the same.
 
 f (x) = x + 1 / x-1
 f (x) ^ - 1 = (x + 1) / (x - 1)
 f (x) = f (x) ^ - 1