Functions
Range of Inverse Trigonometric Functions
JEE Main 2023
Grade 12

Question:

The range of $f(x) = 4 \sin^{-1}\left(\frac{x^2}{x^2 + 1}\right)$ is:
(1) $[0, \pi)$
(2) $[0, 2\pi)$
(3) $(0, 2\pi)$
(4) $[0, \pi]$

Step-by-Step Solution

Key Concept: Note that $x^2/(x^2 + 1) \in [0, 1)$ for all real $x$. Apply the range of $\sin^{-1}$ on $[0, 1)$, then multiply by 4.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)

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