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If (f:\mathbb{R}\to \mathbb{R}), (f(x)=x^3+x), what is the correct statement about (f)?यदि (f:\mathbb{R}\to \mathbb{R}), (f(x)=x^3+x), तो (f) के बारे में सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Ontoआच्छादक है
Step 1: (x^3+x) is a continuous increasing function because (3x^2+1>0). Step 2: As (x\to \infty), the value goes to (\infty), and as (x\to -\infty), it goes to (-\infty). Step 3: Such cubic functions cover all real values.चरण 1: (x^3+x) एक सतत बढ़ता हुआ फलन है क्योंकि (3x^2+1>0)। चरण 2: (x\to \infty) पर मान (\infty) और (x\to -\infty) पर मान (-\infty) की ओर जाता है। चरण 3: ऐसे घन फलन पूरे (\mathbb{R}) को ढकते हैं।
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