For x ≥ 1 , the value of f(x) = 2 ^-1 x + ^-1 2x/1+x^2 is: - Mathematics MCQ Mathematics Mock Test - 10 2026 | ExamTest.live

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For x \geq 1, the value of f (x) = 2 tan^{- 1} x + sin^{- 1} \frac{2 x}{1 + x ^{2}} is:

Solution & Step-by-step Explanation

We know the identity for sin^{- 1} \frac{2 x}{1 + x ^{2}} : sin^{- 1} \frac{2 x}{1 + x ^{2}} = 2 tan^{- 1} x for ∣ x ∣ \leq 1 . sin^{- 1} \frac{2 x}{1 + x ^{2}} = π - 2 tan^{- 1} x for x > 1 .For x = 1, sin^{- 1} (1) = π /2 and π - 2 tan^{- 1} (1) = π - 2 (π /4) = π /2 .So for x \geq 1 : f (x) = 2 tan^{- 1} x + (π - 2 tan^{- 1} x) = π .

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For x \geq 1, the value of f (x) = 2 tan^{- 1} x + sin^{- 1} \frac{2 x}{1 + x ^{2}} is:

4 tan^{- 1} x

\frac{π}{2}

π

2 π

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