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

Explanation

We have `f(x)=(1)/([x]^(2)-7[x]-8)`
Clearly f(x) is not defined if `[x]^(2)-7[x]-8=0`
`implies ([x]-8)([x]+1)=0`
`implies[x]= -1 " or " 8`
`implies x in [-1,0] " or " x in [8,9)`
So, domain of f(x) is `(-oo,-1) cup [0,8) cup [9,oo)`