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If (f:\mathbb{R}\to \mathbb{R}), (f(x)=x+\sin x), which statement is correct about (f)?यदि (f:\mathbb{R}\to \mathbb{R}), (f(x)=x+\sin x), तो (f) के बारे में कौन सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Ontoआच्छादक है
Step 1: (x+\sin x) is continuous. Step 2: As (x\to\infty), it goes to (\infty), and as (x\to-\infty), it goes to (-\infty), because the (x)-term dominates. Step 3: When a bounded trigonometric term is added to (x), check end behavior.चरण 1: (x+\sin x) सतत फलन है। चरण 2: (x\to\infty) पर यह (\infty) और (x\to-\infty) पर (-\infty) की ओर जाता है क्योंकि (x) वाला भाग प्रमुख है। चरण 3: सीमित त्रिकोणमितीय भाग के साथ (x) जुड़ा हो तो अंत व्यवहार देखें।
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