If the function f : R → A defined as f x = sin - 1 ⁡ x 1 + x 2 is a surjective function, then the set A is

Question

If the function f : R → A defined as f x = sin - 1 ⁡ x 1 + x 2 is a surjective function, then the set A is, – π 6 , π 6, – π 2 , π 2, – π 3 , π 6, 0 , π 3

MARKS App · Accepted Answer

Let y = x 1 + x 2 ⇒ y x 2 - x + y = 0 ∵ x ∈ R , hence D ≥ 0 ⇒ - 1 2 - 4 y 2 ≥ 0 ⇒ y ∈ - 1 2 , 1 2 i.e. sin - 1 ⁡ y ∈ sin - 1 ⁡ - 1 2 , sin - 1 ⁡ 1 2 Hence, the range of f x ∈ - π 6 , π 6 ≡ A

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