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The function f x = x 1 + | x | is

Options

  1. Astrictly increasing
  2. Bstrictly decreasing
  3. Cneither increasing nor decreasing
  4. Dnot differentiable at x = 0

Correct answer

A. strictly increasing

Step-by-step solution

Given, f x = x 1 + | x | ∴       f ′ x = 1 + x . 1 - x . x x 1 + x 2 = 1 1 + x 2 > 0   ∀ x ∈ R ⇒       f ( x ) is strictly increasing

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