Inverse Trigonometric Functions
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
The domain of $f(x) = \cos^{-1}(x^2 - 4)$ is:
(a) $[-\sqrt{5}, -\sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]$
(b) $[-\sqrt{5}, \sqrt{5}]$
(c) $[-\sqrt{3}, \sqrt{3}]$
(d) $[-5, 5]$
Step-by-Step Solution
3 \le x^2 \le 5 \Rightarrow x \in [-\sqrt{5}, -\sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $[-\sqrt{5}, -\sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]$: 1.0 Mark
Correct Answer: $[-\sqrt{5}, -\sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]$
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