Which of the following is the range of the function \(y=\frac{1}{2+\sin x}\)?
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Answer and explanation
Correct answer: \(\left[\frac{1}{3},1\right]\)
Since \(-1\le\sin x\le1\), the denominator lies from 1 to 3. Taking reciprocals of positive values reverses the bounds, giving \(\frac13\le y\le1\). Exam tip: check whether endpoint values are attained.
Frequently asked questions
What is the correct answer to this question?
\(\left[\frac{1}{3},1\right]\)
Why is this the correct answer?
Since \(-1\le\sin x\le1\), the denominator lies from 1 to 3. Taking reciprocals of positive values reverses the bounds, giving \(\frac13\le y\le1\). Exam tip: check whether endpoint values are attained.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Domain, range, and graphs of trigonometric functions.
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