Q50 / 120 · VITEEE 2017 · Mathematics

The range of the function $f(x)=\frac{1}{2-\cos 3 x}$ is

  • A
    $(-2, \infty)$
  • B
    $\quad[-2,3]$
  • Correct answer
    C
    $\left[\frac{1}{3}, 1\right]$
  • D
    $\left(\frac{1}{2}, 1\right)$

Solution

We have $-1 \leq \cos 3 x \leq 1 \Rightarrow-1 \leq-\cos 3 x \leq 1$ Add ' 2 ' on both side $\begin{array}{l} 1 \leq 2-\cos 3 x \leq 3 \\ \Rightarrow 1 \geq \frac{1}{2-\cos 3 x} \geq \frac{1}{3} \end{array}$

Hence, the correct answer is option: 'C'.

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