Let f:-1,1→B be a function defined as fx=cot^(-1)⁡2x/(√31+x^2). If f is both one-one and onto, then B is the interval

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MARKS Content Team · Accepted Answer

Correct answer: (C) (π)/3,(2π)/3. Let, y=2x/(√31+x^2) ⇒√3yx^2-2x+√3y=0 ∵x∈R⇒D≥0 ⇒4-12y^2≥0⇒y∈(-1√3,1√3⇒-1√3≤2x)/(√31+x^2)≤1√3 ⇒cot^(-1)⁡-1√3≥cot^(-1)⁡2x/(√31+x^2)≥cot^(-1)⁡1√3 (2π)/3≥fx≥(π)/3

Let $f : [- 1, 1] \to B$ be a function defined as $f (x) = \cot^{- 1} \frac{2 x}{\sqrt{3} (1 + x^{2})}$ . If $f$ is both one-one and onto, then $B$ is the interval

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More Functions Questions

Let f:-1,1→B be a function defined as fx=cot-1⁡2x31+x2. If f is both one-one and onto, then B is the interval

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More Functions Questions

Let $f : [- 1, 1] \to B$ be a function defined as $f (x) = \cot^{- 1} \frac{2 x}{\sqrt{3} (1 + x^{2})}$ . If $f$ is both one-one and onto, then $B$ is the interval