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NTA Abhyas JEE Main2020MathematicsFunctionsPractice

If f x = cos ⁡ x + sin ⁡ x and g x = x 2 - 1 , then g f x is injective in the interval

Options

  1. A0 , π 2
  2. B– π 4 , π 4
  3. C– π 2 , π 2
  4. D0 , π

Correct answer

B. – π 4 , π 4

Step-by-step solution

g f x = sin ⁡ x + cos ⁡ x 2 - 1 = sin ⁡ 2 x Now, sin ⁡ 2 x is injective if 2 x ∈ n π - π 2 , n π + π 2 ⇒ x ∈ n π 2 - π 4 , n π 2 + π 4   ∀ n ∈ Z

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