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NTA Abhyas JEE Main2020MathematicsFunctionsPractice

Which of the following functions is injective?

Options

  1. Af x = x 2 + 3 , x ∈ - ∞ , ∞
  2. Bf x = x + 1 , x ∈ 2 , ∞
  3. Cf x = x - 4 x - 5 , x ∈ ∞ , 5
  4. Df x = 4 x 2 + 3 x - 5 4 + 3 x + 5 x 2 , x ∈ - ∞ , ∞

Correct answer

B. f x = x + 1 , x ∈ 2 , ∞

Step-by-step solution

The function f x = x 2 + 3 ,    x ∈ - ∞ ,   ∞ is not injective as f 1 = f - 1 but 1 ≠ - 1 . The function f x = x - 4 x - 5 ,    x ∈ - ∞ ,   5 is not injective as f 4 = f 5 but 4 ≠ 5 The function f x = 4 x 2 + 3 x - 5 4 + 3 x + 5 x 2 ,    x ∈    - ∞ ,   ∞ is not injective as f 0 = f - 27 41 but 0 ≠ - 27 41 For the function, f x = x + 1 ,   x ∈ 2 ,   ∞ Let f x = f

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