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If (f:\mathbb{R}\to \mathbb{R}), (f(x)=x^5-x), what type is (f)?यदि (f:\mathbb{R}\to \mathbb{R}), (f(x)=x^5-x), तो (f) कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Ontoआच्छादक है
Step 1: (x^5-x) is a continuous odd-degree polynomial. Step 2: As (x\to\infty), the value goes to (\infty), and as (x\to-\infty), it goes to (-\infty). Step 3: Even with turning points, continuity and end behavior can cover all of (\mathbb{R}).चरण 1: (x^5-x) सतत विषम घात बहुपद है। चरण 2: (x\to\infty) पर मान (\infty) और (x\to-\infty) पर मान (-\infty) जाता है। चरण 3: बीच में मोड़ हों तो भी सततता और अंत व्यवहार पूरे (\mathbb{R}) को ढक सकते हैं।
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