CUET · MATHS · PYQ PAPER 2023
The range of the function \(f(x)=\frac{1}{3-\sin 4 x}\) is:
- A \(\left[\frac{1}{4}, \frac{1}{2}\right]\)
- B \(\left[\frac{1}{2}, 1\right]\)
- C \(\left[\frac{1}{4}, \frac{3}{4}\right]\)
- D \(\left[\frac{1}{2}, \frac{3}{4}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\frac{1}{4}, \frac{1}{2}\right]\)
Step-by-step Solution
Detailed explanation
\(-1 \le \sin 4x \le 1\) \(2 \le 3 - \sin 4x \le 4\) \(\frac{1}{4} \le \frac{1}{3 - \sin 4x} \le \frac{1}{2}\) Range is \(\left[\frac{1}{4}, \frac{1}{2}\right]\)
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