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Mathematics · 2025 · 2 marks
Inverse Trigonometric FunctionsBasic Concepts of Inverse Trigonometric Functions2 marksApplyvery short answer
CBSE 2025 · Region 5 · Set 3 · Q21
Find the domain of sin^-1( x^2-3).
Find the domain of $\displaystyle \sin ^{-1}\left(\mathrm{x}^{2}-3\right)$.
Marking-scheme solution
Domain of $\displaystyle \sin ^{-1} \mathrm{x}$ is $\displaystyle [-1,1]$
\[\begin{aligned}
& -\mathbf{1} \leq \mathbf{x}^{2}-\mathbf{3} \leq \mathbf{1} \Rightarrow \mathbf{2} \leq \mathbf{x}^{2} \leq \mathbf{4} \\
& \Rightarrow \text { Domain }=[-2,-\sqrt{2}] \cup[\sqrt{2}, 2]
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.