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.

Answer:

f (x) = x + 1 / x-1

f (x) ^ - 1 = (x + 1) / (x - 1)

f (x) = f (x) ^ - 1