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Why is \(f:\mathbb{R}\to\mathbb{R}\), where \(f(x)=e^x\), not onto?फलन \(f:\mathbb{R}\to\mathbb{R}\) जहाँ \(f(x)=e^x\), क्यों आच्छादी नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because negative real numbers are not imagesक्योंकि ऋणात्मक वास्तविक संख्याएँ प्रतिबिंब नहीं हैं
Step 1: The range of (e^x) is \((0,\infty)\). Step 2: The codomain is \(\mathbb{R}\), but values like (-1) are never attained. Step 3: If even one codomain element is missed, the function is not onto.चरण 1: (e^x) का परिसर \((0,\infty)\) होता है। चरण 2: सहप्रांत \(\mathbb{R}\) है लेकिन (-1) जैसे मान कभी नहीं मिलते। चरण 3: एक भी सहप्रांतीय मान छूट जाए तो फलन आच्छादी नहीं होता।
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