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Which of the following is the range of the function \(y=\frac{1}{2+\sin x}\)?फलन \(y=\frac{1}{2+\sin x}\) का परास निम्नलिखित में से कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\left[\frac{1}{3},1\right]\)\(\left[\frac{1}{3},1\right]\)
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.क्योंकि \(-1\le\sin x\le1\), इसलिए \(1\le2+\sin x\le3\)। धनात्मक हर का व्युत्क्रम लेने पर क्रम उलटता है और \(\frac13\le y\le1\) मिलता है। परीक्षा में सिरों को शामिल करना न भूलें।
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