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Choose the correct option for (f:\mathbb{R}\to\mathbb{R}), (f(x)=x+\sin x).फलन (f:\mathbb{R}\to\mathbb{R}), (f(x)=x+\sin x) के लिए सही विकल्प चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is one-oneएकैकी है
Step 1: (f'(x)=1+\cos x), which is never negative. Step 2: The function does not decrease, and the (x) term keeps values separated as inputs move forward. Step 3: A derivative may become zero at points, but being non-negative can help in checking one-one nature.चरण 1: (f'(x)=1+\cos x) है जो कभी ऋणात्मक नहीं होता। चरण 2: फलन घटता नहीं है और (x) वाला भाग आगे बढ़ते हुए मानों को अलग रखता है। चरण 3: अवकलज शून्य हो सकता है पर ऋणात्मक न होना एकैकीता की जाँच में सहायक है।
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