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AP EAMCET · Maths · Inverse Trigonometric Functions

The range of the real valued function \(f(x)=\operatorname{Cos}^{-1}\left(\frac{3}{\sqrt{9 x^2-12 x+22}}\right)\) is

  1. A \(\left(0, \frac{\pi}{4}\right]\)
  2. B \(\left[\frac{\pi}{4}, \frac{\pi}{2}\right)\)
  3. C \([0, \pi]\)
  4. D \(\left[\frac{\pi}{6}, \frac{\pi}{2}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\left[\frac{\pi}{4}, \frac{\pi}{2}\right)\)

Step-by-step Solution

Detailed explanation

\(9 x^2-12 x+22 = (3x-2)^2+18\). \(\min((3x-2)^2+18) = 18\). \(\sqrt{9 x^2-12 x+22} \ge \sqrt{18} = 3\sqrt{2}\). \(0 \(\text{Range of argument } y \text{ is } \left(0, \frac{1}{\sqrt{2}}\right]\).…