AP EAMCET · Maths · Functions
The range of the real valued function
\(f(x)=\frac{15}{3 \sin x+4 \cos x+10}\) is
- A \([0,3]\)
- B \([-1,3]\)
- C \([1,3]\)
- D \([-1,1]\)
Answer & Solution
Correct Answer
(C) \([1,3]\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & -\sqrt{9+16} \leq 3 \sin x+4 \cos x \leq \sqrt{9+16} \\ \Rightarrow & 5 \leq 3 \sin x+4 \cos x+10 \leq 15 \\ \Rightarrow & \frac{1}{15} \leq \frac{1}{3 \sin x+4 \cos x+10} \leq \frac{1}{5} \\ \Rightarrow & 1 \leq \frac{15}{3 \sin x+4 \cos x+10} \leq 3 \\…
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