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

Question

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, 0 , x 6, 0 , π 6, - π 6 , π 6, - π 6 , π 6

MARKS App · Accepted Answer

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

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