AP EAMCET · Maths · Functions
If \(\mathrm{f}: \mathbb{R} \rightarrow \mathrm{A}\), defined by \(\mathrm{f}(\mathrm{x})=\cos \mathrm{x}+\sqrt{3} \sin \mathrm{x}-1\), is an onto function then \(\mathrm{A}=\)
- A \([-1,2]\)
- B \([-\sqrt{3}, \sqrt{3}]\)
- C \([-3,1]\)
- D \([-2,2]\)
Answer & Solution
Correct Answer
(C) \([-3,1]\)
Step-by-step Solution
Detailed explanation
\( \cos x + \sqrt{3} \sin x = 2 \left( \frac{1}{2} \cos x + \frac{\sqrt{3}}{2} \sin x \right) = 2 \sin \left( x + \frac{\pi}{6} \right) \) \( -1 \le \sin \left( x + \frac{\pi}{6} \right) \le 1 \) \( -2 \le 2 \sin \left( x + \frac{\pi}{6} \right) \le 2 \)…
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