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Why is (f:[0,\infty)\to\mathbb{R}), (f(x)=\sqrt{x}), not onto?फलन (f:[0,\infty)\to\mathbb{R}), (f(x)=\sqrt{x}), आच्छादक क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because no negative real value is obtainedक्योंकि कोई ऋणात्मक वास्तविक मान प्राप्त नहीं होता
Step 1: (\sqrt{x}\ge0) for all (x\ge0). Step 2: The codomain (\mathbb{R}) contains negative numbers such as (-2), which are not obtained. Step 3: If the range is smaller than the codomain, the function is not onto.चरण 1: (\sqrt{x}\ge0) सभी (x\ge0) के लिए। चरण 2: सहप्रांत (\mathbb{R}) में ऋणात्मक संख्याएँ भी हैं, जैसे (-2), जो नहीं मिलतीं। चरण 3: परास छोटा और सहप्रांत बड़ा हो तो फलन आच्छादक नहीं होता।
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