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NTA Abhyas JEE Main2020MathematicsFunctionsPractice

Let f : A → B is a function defined by f x = 2 x 1 + x 2 . If the function f x is a bijective function, then the correct statement can be

Options

  1. AA = B = - 1,1
  2. BA = B = - 2,2
  3. CA = - 1,1 , B = - 2,2
  4. DA = - 2,2 , B = - 1,1

Correct answer

A. A = B = - 1,1

Step-by-step solution

∵ f x = 2 x 1 + x 2 Now, f ' x = 1 + x 2 2 − 2 x 2 x 1 + x 2 2 ⇒ 2 1 − x 2 1 + x 2 2 Clearly, f ′ x is injective either for x ∈ - 1,1 or for x ∈ - ∞ , - 1 ∪ 1 , ∞ Now, for x ∈ - 1,1 Range of f x ∈ f - 1 , f 1 ≡ - 1,1

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