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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3+3x), what is the correct reason for being onto?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3+3x) है, तो आच्छादी होने का सही कारण क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: The function is continuous and goes from (-\infty) to (\infty)फलन सतत है और (-\infty) से (\infty) तक मान लेता है
Step 1: (x^3+3x) is a continuous cubic polynomial. Step 2: As (x\to-\infty), it goes to (-\infty), and as (x\to\infty), it goes to (\infty). Step 3: Continuous cubic polynomials are often onto from (\mathbb{R}) to (\mathbb{R}).चरण 1: (x^3+3x) एक सतत घन बहुपद है। चरण 2: (x\to-\infty) पर मान (-\infty) और (x\to\infty) पर मान (\infty) की ओर जाता है। चरण 3: सतत घन बहुपद प्रायः (\mathbb{R}\to\mathbb{R}) पर आच्छादी होता है।
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