Find the domain of the function.
\[
f(x)=\log _{2}\left(\frac{-1}{x-2}\right)
\]

Write your answer as an interval or union of intervals.
Domain: Ø]

Step 1 ：The domain of a function is the set of all possible input values (x-values) which will produce a valid output.

Step 2 ：For the function \(f(x)=\log _{2}\left(\frac{-1}{x-2}\right)\), the argument of the logarithm, \(\frac{-1}{x-2}\), must be greater than zero because you can't take the logarithm of a negative number or zero.

Step 3 ：So, we have the inequality: \(\frac{-1}{x-2} > 0\)

Step 4 ：To solve this inequality, we first consider the denominator (x-2). The denominator cannot be zero, so x ≠ 2.

Step 5 ：Next, we solve the inequality. We multiply both sides by (x-2), but we must remember that if (x-2) is negative, the direction of the inequality will change.

Step 6 ：If x > 2, (x-2) is positive, and the inequality remains the same: -1 > 0, which is not possible.

Step 7 ：If x < 2, (x-2) is negative, and the inequality changes direction: -1 < 0, which is always true.

Step 8 ：So, the solution to the inequality is x < 2.

Step 9 ：Therefore, the domain of the function is \(\boxed{(-\infty, 2)}\).