Question:
The range of the function
\[
f(x) = \frac{1}{2 - \cos 3x}
\]
is
The range of the function
\[
f(x) = \frac{1}{2 - \cos 3x}
\]
is
Show Hint
When evaluating the range of a trigonometric function, first find the range of the trigonometric part and then apply it to the entire expression.
Updated On: Jan 12, 2026
- (-2, ∞)
- [-3, 3]
- [1, 2]
- [1, ∞)
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The Correct Option is D
Solution and Explanation
Step 1: Analyze the behavior of the cosine function.
Since the function involves \( \cos 3x \), which has a range of [-1, 1], the denominator of the function will be in the range [1, 3]. Therefore, the range of the function \( f(x) \) will be [1, ∞).
Step 2: Conclusion.
Thus, the range of the function is [1, ∞).
Final Answer: \[ \boxed{[1, \infty)} \]
Since the function involves \( \cos 3x \), which has a range of [-1, 1], the denominator of the function will be in the range [1, 3]. Therefore, the range of the function \( f(x) \) will be [1, ∞).
Step 2: Conclusion.
Thus, the range of the function is [1, ∞).
Final Answer: \[ \boxed{[1, \infty)} \]
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