Let f : R → B , be a function defined by f x = t a n - 1 2 x 3 1 + x 2 , then f is both one-one and onto when B, is the interval

Step-by-step solution

Let y = 2 x 3 1 + x 2 ⇒ 3 y x 2 - 2 x + 3 y = 0 ∵ x ∈ R ⇒ D ≥ 0 ⇒ 4 - 12 y 2 ≥ 0 ⇒ y ∈ - 1 3 , 1 3 - 1 3 ≤ 2 x 3 1 + x 2 ≤ 1 3 ⇒ t a n - 1 - 1 3 ≤ t a n - 1 2 x 3 1 + x 2 ≤ t a n - 1 1 3 - π 6 ≤ f x ≤ π 6