Verified Solution • 2025–26 Session moderate

QJEEM23Mab8d8: JEE Main 2023 Mathematics - Class 11 JEEM23Mab8d8 Solution: The range of f ( x ) = 4 sin − 1 ⁡ ( x 2 x 2 + 1 ) is

The range of $f (x) = 4 \sin^{- 1} (\frac{x^{2}}{x^{2} + 1})$ is

Multiple Choice Options

A [0,2π]
B [0,2π)
C [0,π)
D [0,π]

Step-by-Step Verified Solution

\begin{aligned} \frac{x^{2}}{1 + x^{2}} = 1 - \frac{1}{1 + x^{2}} < 1 \\ ∴ & 0 \leq \frac{x^{2}}{1 + x^{2}} < 1 \\ \Rightarrow & 0 \leq \sin^{- 1} (\frac{x^{2}}{1 + x^{2}}) < \frac{π}{2} \\ \Rightarrow & 0 \leq 4 \sin^{- 1} (\frac{x^{2}}{1 + x^{2}}) < 2 π \end{aligned}

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