The domain of definition of function f(x)=log x2-5x-24  -x-2,is

Here,x2-5x-24>x+2 is equivalent to the collection of two system of inequations.Case I x2-5x-24≥0 and x+2<0 ⇒     (x-8)(x+3)≥0 and x<-2 ⇒              x≤-3                  .....(i)Case IIx2-5x-24≥0,x+2≥0 and            x2-5x-24>x+22 ⇒      x∈(-∞,-3]∪[8,∞),x∈[-2,∞) and   x2-5x-24>x2+4x+4 ⇒          9x<-28 ⇒             x<-289 ∴       No solution i.e., x∈ϕ            ....(ii) From Eqs.(i) and (ii), we get x∈(-∞,-3]