Find the domain of the function : `f(x)=(log)_((x-4))(x^2-11 x+24)`

Answer

`(8,oo)`

Explanation

`f(x)=log_(x-4)(x^(2)-11x+24).`
`f(x)` is defined if
`x-4 gt 0 " and " ne 1 " and " x^(2)-11x+24 gt0`
or `x gt 4 " and " ne 5 " and " (x-3)(x-8) gt 0`
i.e., `x gt 4 " and " ne 5 " and " x lt 3 " or " x gt 8`
or ` x gt 8`
or domain`(y)=(8,oo)`