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JEE Main20199 Apr 2019Evening ShiftMathematicsFunctionsActual

The domain of the definition of the function f x = 1 4 - x 2 + l o g 10 x 3 - x is:

Options

  1. A- 1,   0 ∪ 1 ,   2 ∪ 2 ,   ∞
  2. B( 1 ,   2 ) ∪ 2 ,   ∞
  3. C- 2 ,   - 1 ∪ - 1 ,   0 ∪ 2 ,   ∞
  4. D- 1 ,   0 ∪ 1 ,   2 ∪ 3 ,   ∞

Correct answer

A. - 1,   0 ∪ 1 ,   2 ∪ 2 ,   ∞

Step-by-step solution

We know that log 10 g x is defined when g x > 0 and for a fraction to be defined its denominator must be non-zero. Thus, the given function is defined only when x 3 - x > 0 and 4 - x 2 ≠ 0 ⇒ x x - 1 x + 1 > 0 and x ≠ 2 ,   - 2 The wavy curve for the inequality is ⇒ x ∈ - 1 ,   0 ∪ 1 ,   ∞ and x ≠ 2 ,   - 2 . Hence, domain is - 1 ,   0 ∪ 1 ,   2 ∪ 2 ,   ∞ .

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