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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If the function f : R → A defined as f x = tan - 1 ⁡ 2 x 3 1 + x 6 is a surjective function, then the set A is equal to

Options

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

Correct answer

B. – π 4 , π 4

Step-by-step solution

Let, x 3 = t ∈ R Let, y = 2 t 1 + t 2 ⇒ y t 2 - 2 t + y = 0 ∵ t ∈ R , hence D ≥ 0 ⇒ - 2 2 - 4 y 2 ≥ 0 ⇒ y ∈ - 1,1 tan - 1 ⁡ y ∈ tan - 1 ⁡ - 1 , tan - 1 ⁡ 1 Hence, the range of f x ∈ - π 4 , π 4 ≡ A

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