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Mathematics · 2025 · 2 marks
Inverse Trigonometric FunctionsBasic Concepts of Inverse Trigonometric Functions2 marksApplyvery short answer
CBSE 2025 · Region 5 · Set 1 · Q21
Find the domain of the function f( x )= cos^-1( x^2-4).
Find the domain of the function $\displaystyle f(\mathrm{x})=\cos ^{-1}\left(\mathrm{x}^{2}-4\right)$.
Marking-scheme solution
Domain of $\displaystyle \cos ^{-1} \mathrm{x}$ is $\displaystyle [-1,1]$
\[\begin{array}{r}
\Rightarrow-1 \leq \mathrm{x}^{2}-4 \leq 1 \Rightarrow 3 \leq \mathrm{x}^{2} \leq 5 \\
\Rightarrow \mathrm{x} \in[-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]
\end{array}
\]
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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.