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

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

  1. A

    (-,-3]

  2. B

    (-,-3][8,)

  3. C

    -,-289

  4. D

    None of these

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    Solution:

    Here,
    x2-5x-24>x+2 is equivalent to the collection of two system of inequations.
    Case I
     x2-5x-240 and x+2<0      (x-8)(x+3)0 and x<-2               x-3                  .....(i)
    Case II
    x2-5x-240,x+20 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., xϕ            ....(ii) From Eqs.(i) and (ii), we get x(-,-3]



     

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