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AP EAMCET20228 Jul 2022Evening ShiftMathematicsFunctionsActual

The domain of the real valued function f(x)= 2-|x| 3-|x| is

Options

  1. A(- , )
  2. B(- ,-3) (2, )
  3. C(- ,-3] (-2,2) [3, )
  4. D(- ,-3) [-2,2] (3, )

Correct answer

D. (- ,-3) [-2,2] (3, )

Step-by-step solution

Given, f(x)= 2-|x| 3-|x| For f(x) to be defined, 2-|x| 3-|x| 0 Case I If x 0 , then 2-x 3-x 0 x-2 x-3 0 Thus, x (- , 2] (3, ) ...(i) Case II If x Thus, x (- ,-3) [-2, ) ...(ii) Case III 3-|x| 0 |x| 3 x 3,-3 ...(iii) From Eqs. (i), (ii) and (iii), we get x (- ,-3) [-2,2] (3, )

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