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Which statement is correct for (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3+x^2+x+1)?फलन (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3+x^2+x+1), के लिए कौन-सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is ontoयह आच्छादक है
Step 1: This is an odd-degree polynomial with leading term (x^3). Step 2: As (x\to\infty), the value goes to (\infty), and as (x\to-\infty), it goes to (-\infty). Step 3: A continuous odd-degree polynomial from (\mathbb{R}) to (\mathbb{R}) is generally onto.चरण 1: यह विषम घात वाला बहुपद है जिसका अग्र पद (x^3) है। चरण 2: (x\to\infty) पर मान (\infty) और (x\to-\infty) पर मान (-\infty) की ओर जाता है। चरण 3: सतत विषम घात बहुपद (\mathbb{R}\to\mathbb{R}) में सामान्यतः आच्छादक होता है।
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