The domain of definition of function f(x)=log x2-5x-24 -x-2,is
(-∞,-3]
(-∞,-3]∪[8,∞)
-∞,-289
None of these
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]