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Let f x = 2 1 x - 1 2 1 x + 1 : x ≠ 0 0 : x = 0 , then f x is

Options

  1. Acontinuous and differentiable at x = 0
  2. Bcontinuous but not differentiable at x = 0
  3. Cdifferentiable but not continuous at x = 0
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

For function f x at x = 0 L.H.L. = l i m h → 0 + f 0 - h = l i m h → 0 + 2 - 1 h - 1 2 - 1 h + 1 = 0 - 1 0 + 1 = - 1 R.H.L. = l i m h → 0 + f 0 + h = l i m h → 0 + 2 1 h - 1 2 1 h + 1 = l i m h → 0 + 1 - 2 - 1 h 1 + 2 - 1 h = 1 - 0 1 + 0 = 1 Since, l i m h → 0 + f 0 - h ≠ l i m h → 0 + f 0 - h , therefore, f x is not continuous and not differentiable at x = 0 .

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