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Consider f x = x + - x   x ≠ 2 λ x = 2 , where · denotes the greatest integer function. If f x is continuous at x = 2 , then the value of λ is equal to

Options

  1. A- 1
  2. B0
  3. C1
  4. DNo value is possible

Correct answer

A. - 1

Step-by-step solution

lim x → 2 - ⁡ f x = lim x → 2 - ⁡ x + - x = lim x → 2 - ⁡ x + lim x → 2 - ⁡ - x = 1 - 2 = - 1 lim x → 2 + ⁡ f x = lim x → 2 + ⁡ x + - x = lim x → 2 + ⁡ x + lim x → 2 + ⁡ - x = 2 + - 3 = - 1 ∴ λ = - 1 wil make f continuous at x = 2

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