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

Question

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, – π 2 , π 2, – π 4 , π 4, – π 2 , π 2, 0 , π 4

MARKS App · Accepted Answer

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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