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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3+2x), what is the correct reason that (f) is onto?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3+2x) है, तो (f) के आच्छादी होने का सही कारण क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is increasing and extends in both real directionsयह लगातार बढ़ता है और सभी वास्तविक दिशाओं में जाता है
Step 1: (f'(x)=3x^2+2>0), so the function is increasing. Step 2: As (x\to\infty), (f(x)\to\infty), and as (x\to-\infty), (f(x)\to-\infty). Step 3: Such a continuous increasing function covers all of (\mathbb{R}).चरण 1: (f'(x)=3x^2+2>0), इसलिए फलन बढ़ता है। चरण 2: (x\to\infty) पर (f(x)\to\infty) और (x\to-\infty) पर (f(x)\to-\infty)। चरण 3: ऐसा सतत बढ़ता फलन (\mathbb{R}) को पूरा ढकता है।
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