Please Find f^-1(x)

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). To get f^-1(x) we interchange x and y: x = 8y/(y -2) and now we solve for y: xy - 2x = 8y;

xy - 8y = 2x; y(x - 8) = 2x; y = 2x/(x - 8); f^-1(x) = 2x/(x - 8), x ≠ 8.

Answer 2

Whenever -1 is a power it =1/; so f^-1(x)=x/f.