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TS EAMCET · Maths · Functions

If \(f: R \rightarrow R\) and is defined by \(f(x)=\frac{1}{2-\cos 3 x}\) for each \(x \in R\), then the range of \(f\) is

  1. A \((1 / 3,1)\)
  2. B \([1 / 3,1]\)
  3. C \((1,2)\)
  4. D \([1,2]\)
Verified Solution

Answer & Solution

Correct Answer

(B) \([1 / 3,1]\)

Step-by-step Solution

Detailed explanation

\begin{array}{lrl}\text { Given, } & f(x)= & \frac{1}{2-\cos 3 x} \\ \because & & -1 \leq \cos 3 x \leq 1 \\ \Rightarrow & 1 \leq-\cos 3 x \leq-1 \\ \Rightarrow & 2+1 & \leq 2-\cos 3 x \leq 2-1 \\ \Rightarrow & 3 \leq 2-\cos 3 x \leq 1 \\ \Rightarrow & \frac{1}{3} \leq…