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Manipal MET2010MathematicsFunctions

The domain of the function f(x)= 9-x^2 ⁻¹(3-x) is

Options

  1. A(2,3)
  2. B[2,3)
  3. C(2,3]
  4. DNone of these

Correct answer

B. [2,3)

Step-by-step solution

9-x^2 is defined for 9-x^2 0 (3-x)(3+x) 0 (x-3)(x+3) 0...(i) -3 x 3 ⁻¹(3-x) defined for -1 3-x 1 -4 -x -2 2 x 4...(ii) Also, ⁻¹(3-x) 0 3-x 0 or x 3...(iii) From Eqs. (i), (ii) and (iii), we get The domain of f=([1-3,3] [2,4])- 3 =[2,3)

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