Find f^-1(x) and state the restrictions

Question

f(x)= 8x/x-2, x= is not equal to 2

f^-1(x)=?

State any restrictions on the domain of f^-1(x).

1. x > 2
2. x>8
3. X= NOT EQUAL TO 8
4. X= NOT EQUAL TO 2
5. There are no restrictions on the domain

Answer 1

y = 8x/(x-2)

xy-2y = 8x

xy-8x = 2y

x(y-8) = 2y

x = 2y/(y-8)

f^-1(x) = 2x/(x-8)

The domain is x ≠8

(Note that the x not equal to 2 in the original domain becomes the horizontal asymptote; also, y = 8 is the horizontal asymptote with the original function)