Find the domain of the function `f(x)=(1)/([x]^(2)-7[x]-8)`, where [.] represents the greatest integer function.

Explanation

To find the domain of the function \( f(x) = \frac{1}{[x]^2 - 7[x] - 8} \), where \([x]\) denotes the greatest integer function (also known as the floor function), we need to determine the values of \( x \) for which the function is defined. The function is undefined when the denominator equals zero. Therefore, we need to solve the equation:

\[ [x]^2 - 7[x] - 8 = 0 \]

### Step 1: Solve the quadratic equation

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