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Why is (f:\mathbb{R}\to\mathbb{R}), where (f(x)=|x|+x), not onto?फलन (f:\mathbb{R}\to\mathbb{R}) जहाँ (f(x)=|x|+x), आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because negative values are not attainedक्योंकि ऋणात्मक मान नहीं मिलते
Step 1: If (x<0), then (|x|+x=-x+x=0). Step 2: If (x\ge0), then (|x|+x=2x), so values are non-negative. Step 3: Use piecewise behavior to find the range.चरण 1: यदि (x<0), तो (|x|+x=-x+x=0)। चरण 2: यदि (x\ge0), तो (|x|+x=2x), इसलिए मान गैरऋणात्मक हैं। चरण 3: खंडों में परिभाषित व्यवहार से परिसर निकालें।
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