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The range of the function $f(x)=\frac{1}{2-\cos 3 x}$ is
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1246 Upvotes
Verified Answer
The correct answer is:
$\left[\frac{1}{3}, 1\right]$
We have
$-1 \leq \cos 3 x \leq 1 \Rightarrow-1 \leq-\cos 3 x \leq 1$
Add ' 2 ' on both side
$\begin{array}{l}
1 \leq 2-\cos 3 x \leq 3 \\
\Rightarrow 1 \geq \frac{1}{2-\cos 3 x} \geq \frac{1}{3}
\end{array}$
$-1 \leq \cos 3 x \leq 1 \Rightarrow-1 \leq-\cos 3 x \leq 1$
Add ' 2 ' on both side
$\begin{array}{l}
1 \leq 2-\cos 3 x \leq 3 \\
\Rightarrow 1 \geq \frac{1}{2-\cos 3 x} \geq \frac{1}{3}
\end{array}$
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